<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author><author><style face="normal" font="default" size="100%">Barahona, Pedro</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">K-Best Feasible Clusters- Ranking optimal solutions from an infeasible LP</style></title><secondary-title><style face="normal" font="default" size="100%">under revision</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Matemática Industrial em Rede</style></title><secondary-title><style face="normal" font="default" size="100%">Gazeta de Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><publisher><style face="normal" font="default" size="100%">SPM</style></publisher><volume><style face="normal" font="default" size="100%">181</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O admirável Mundo Novo do Big Data</style></title><secondary-title><style face="normal" font="default" size="100%">Gazeta de Matemática</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><publisher><style face="normal" font="default" size="100%">SPM</style></publisher><volume><style face="normal" font="default" size="100%">182</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>36</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Copositive Optimization Course -Part 1</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/paca/files/pamaral_costparis_part1.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">CNAM Paris</style></publisher><pages><style face="normal" font="default" size="100%">1-84</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Copositive Optimization Course -Part 2</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://docentes.fct.unl.pt/sites/default/files/paca/files/pamaral_costparis_part2.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">CNAM Paris</style></publisher><pages><style face="normal" font="default" size="100%">1-44</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author><author><style face="normal" font="default" size="100%">Tiago Cardal Pais</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Compromise ratio with weighting functions in a Tabu Search multi-criteria approach to examination timetabling</style></title><secondary-title><style face="normal" font="default" size="100%">Computers &amp; Operations Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><volume><style face="normal" font="default" size="100%">72</style></volume><pages><style face="normal" font="default" size="100%">160–174</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Salmerón, J.M.G.</style></author><author><style face="normal" font="default" size="100%">Amaral, P.</style></author><author><style face="normal" font="default" size="100%">Casado, L.G.</style></author><author><style face="normal" font="default" size="100%">Hendrix, E.M.T.</style></author><author><style face="normal" font="default" size="100%">Żilinskas, J</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On Regular Simplex Refinement in Copositivity Detection</style></title><secondary-title><style face="normal" font="default" size="100%">XIII global optimization workshop GOW2016 4-8 September 2016</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><pages><style face="normal" font="default" size="100%">163–166</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula A.</style></author><author><style face="normal" font="default" size="100%">Bomze, Immanuel M.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Copositivity-based approximations for mixed-integer fractional quadratic optimization</style></title><secondary-title><style face="normal" font="default" size="100%">Pacific Journal of Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2015</style></year></dates><number><style face="normal" font="default" size="100%">2</style></number><volume><style face="normal" font="default" size="100%">11</style></volume><pages><style face="normal" font="default" size="100%">225-238</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Isabel Gomes</style></author><author><style face="normal" font="default" size="100%">Santos, Jorge</style></author><author><style face="normal" font="default" size="100%">Luís Cavique</style></author><author><style face="normal" font="default" size="100%">Nelson C. Martins</style></author><author><style face="normal" font="default" size="100%">Manuel Vieira</style></author><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author><author><style face="normal" font="default" size="100%">Raquel Barreira</style></author><author><style face="normal" font="default" size="100%">Fernandes, Vitor H.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AMT (airline maintenance technicians) timetabling optimization- ESGI101 - Relatório Final- TAP-AMT</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><publisher><style face="normal" font="default" size="100%">ESGI 101, FCT, UNL, 2014</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author><author><style face="normal" font="default" size="100%">Bomze, Immanuel M.</style></author><author><style face="normal" font="default" size="100%">Júdice, Joaquim</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Copositivity and constrained fractional quadratic problems</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematical Programming</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><number><style face="normal" font="default" size="100%">1-2</style></number><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><volume><style face="normal" font="default" size="100%">146</style></volume><pages><style face="normal" font="default" size="100%">325–350</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On Fractional Quadratic Problems</style></title><secondary-title><style face="normal" font="default" size="100%">XII global optimization workshop MAGO 2014, 1-4 September 2014</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2014</style></year></dates><pages><style face="normal" font="default" size="100%">113–116</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Eligius M. T. Hendrix</style></author><author><style face="normal" font="default" size="100%">Leocadio G. Casado</style></author><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Global Optimization Simplex Bisection Revisited Based on Considerations by Reiner Horst</style></title><secondary-title><style face="normal" font="default" size="100%">Lecture Notes in Computer Science  - ICSSA2012  </style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://link.springer.com/chapter/10.1007%2F978-3-642-31137-6_12</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">7335</style></volume><pages><style face="normal" font="default" size="100%">159-173</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, the use of non-optimality spheres in a simplicial branch and bound (B&amp;amp;B) algorithm is investigated. In this context, some considerations regarding the use of bisection on the longest edge in relation with ideas of Reiner Horst are reminded. Three arguments highlight the merits of bisection of simplicial subsets in  B&amp;amp;B schemes.&lt;/p&gt;
</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Tiago Cardal Pais</style></author><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Managing the tabu list length using a fuzzy inference system: an application to examination timetabling</style></title><secondary-title><style face="normal" font="default" size="100%">Annals of Operations Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><number><style face="normal" font="default" size="100%">1</style></number><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><volume><style face="normal" font="default" size="100%">194</style></volume><pages><style face="normal" font="default" size="100%">341–363</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">An algorithmic approach to the management of the Body-in-White (BIW) in Model Mix Solution to WOLKSWAGEN-Autoeuropa</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><publisher><style face="normal" font="default" size="100%">Departamento de Matemática - FCT UNL</style></publisher><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author><author><style face="normal" font="default" size="100%">Fernandes, L. M.</style></author><author><style face="normal" font="default" size="100%">Júdice, J.</style></author><author><style face="normal" font="default" size="100%">Sherali, H. D.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On optimal zero-preserving corrections for inconsistent linear systems</style></title><secondary-title><style face="normal" font="default" size="100%">Journal of Global Optimization</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><volume><style face="normal" font="default" size="100%">45</style></volume><pages><style face="normal" font="default" size="100%">645-666</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose objective function is a sum of fractional functions. A branch-and-bound algorithm for solving this nonconvex program is proposed, based on suitably overestimating the denominator function for computing lower bounds. Computational experience is presented to demonstrate the efficacy of this approach.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gomes, Margarida M</style></author><author><style face="normal" font="default" size="100%">Rita A. Ribeiro</style></author><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Reducing the Number of Membership Functions in Linguistic Variables</style></title><secondary-title><style face="normal" font="default" size="100%">Livro de actas do 14º Congresso da Associação Portuguesa de Investigação Operacional, IO 2009, 7-9 September 2009</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><pages><style face="normal" font="default" size="100%">75–82</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Pais, Tiago C</style></author><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Tabu Search Based Approach For Exams Timetabling Problem</style></title><secondary-title><style face="normal" font="default" size="100%">Livro de actas do 14º Congresso da Associação Portuguesa de Investigação Operacional, IO 2009, 7-9 September 2009</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2009</style></year></dates><pages><style face="normal" font="default" size="100%">155–162</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Tiago Cardal Pais</style></author><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Managing the tabu list length using a fuzzy inference system: an application to exams timetabling</style></title><secondary-title><style face="normal" font="default" size="100%">The 7th International Conference for the Practice and Theory of Automated Timetabling</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://patatconference.org/patat2008/proceedings/Amaral-HC2c.pdf</style></url></web-urls></urls><pages><style face="normal" font="default" size="100%">1–6</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author><author><style face="normal" font="default" size="100%">Júdice, Joaquim</style></author><author><style face="normal" font="default" size="100%">Sherali, Hanif D</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A reformulation–linearization–convexification algorithm for optimal correction of an inconsistent system of linear constraints</style></title><secondary-title><style face="normal" font="default" size="100%">Computers &amp; Operations Research</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><number><style face="normal" font="default" size="100%">5</style></number><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><volume><style face="normal" font="default" size="100%">35</style></volume><pages><style face="normal" font="default" size="100%">1494–1509</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Tiago Cardal Pais</style></author><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Using weight aggregation in tabu search for multiobjective exams timetabling problem</style></title><secondary-title><style face="normal" font="default" size="100%">MTISD 2008. Methods, Models and Information Technologies for Decision Support Systems</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2008</style></year></dates><number><style face="normal" font="default" size="100%">1</style></number><volume><style face="normal" font="default" size="100%">1</style></volume><pages><style face="normal" font="default" size="100%">81–84</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author><author><style face="normal" font="default" size="100%">P. Barahona</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Framework for Optimal Correction of Inconsistent Linear Constraints</style></title><secondary-title><style face="normal" font="default" size="100%">Constraints</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><volume><style face="normal" font="default" size="100%">10:1</style></volume><pages><style face="normal" font="default" size="100%">67-86</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The problem of inconsistency between constraints often arises in practice as the result, among others, of the complexity of real models or due to unrealistic requirements and preferences. To overcome such inconsistency two major actions may be taken: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as ``model corre\-ction&quot; is the problem we address in this paper in the context of linear constraints over the reals. The correction of the right hand side alone, which is very close to a fuzzy constraints approach, was one of the first proposals to deal with inconsistency, as it may be mapped into a linear problem.  The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, that provide corrections with quite rigid patterns, the optimization of the important Frobenius norm was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global   minimizer.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">&lt;p&gt;n/a&lt;/p&gt;
</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author><author><style face="normal" font="default" size="100%">Barahona, Pedro</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Connections between the total least squares and the correction of an infeasible system of linear inequalities</style></title><secondary-title><style face="normal" font="default" size="100%">Linear algebra and its applications</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><volume><style face="normal" font="default" size="100%">395</style></volume><pages><style face="normal" font="default" size="100%">191–210</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author><author><style face="normal" font="default" size="100%">P. Barahona</style></author></authors><secondary-authors><author><style face="normal" font="default" size="100%">Pascal Van Hentenryck</style></author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">On Optimal Correction of Inconsistent Linear Constraints</style></title><secondary-title><style face="normal" font="default" size="100%">Principles and Practice of Constraint Programming, CP'2002</style></secondary-title><tertiary-title><style face="normal" font="default" size="100%">Lecture Notes in Computer Science</style></tertiary-title></titles><dates><year><style  face="normal" font="default" size="100%">2002</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><volume><style face="normal" font="default" size="100%">2470</style></volume><pages><style face="normal" font="default" size="100%">33-46</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In practice one has often to deal with the problem of inconsistency between constraints, as the result, among others, of the comple\-xi\-ty of real models. To overcome these conflicts we can outline two major \mbox{actions}: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as ``model corre\-ction&quot; is the problem we address in this paper. The correction of the right hand side alone was one of the first approaches. The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, the optimization of the important Frobenius was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global minimizer.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Contribuições para o estudo de sistemas lineares inconsistentes</style></title><secondary-title><style face="normal" font="default" size="100%">PhD Disertation, Faculty of Science and Technology, UNL, Lisbon, Portugal (in Portuguese)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2001</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author><author><style face="normal" font="default" size="100%">Trosset, M.W.</style></author><author><style face="normal" font="default" size="100%">P. Barahona</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Correcting an inconsistent system of linear inequalities by nonlinear programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2000</style></year></dates><number><style face="normal" font="default" size="100%">00-27</style></number><publisher><style face="normal" font="default" size="100%">Department of Computational &amp; Applied Mathematics, Rice University</style></publisher><pub-location><style face="normal" font="default" size="100%">Houston, TX 77005</style></pub-location><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author><author><style face="normal" font="default" size="100%">Trosset, M.W.</style></author><author><style face="normal" font="default" size="100%">P. Barahona</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Correcting an Inconsistent System of Linear Inequalities by Nonlinear Programming</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2000</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.caam.rice.edu/tech_reports/2000_abstracts.html#TR00-27</style></url></web-urls></urls><number><style face="normal" font="default" size="100%">00-27</style></number><publisher><style face="normal" font="default" size="100%">Department of Computational &amp; Applied Mathematics, Rice University</style></publisher><pub-location><style face="normal" font="default" size="100%">TX 77005, Houston</style></pub-location><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author><author><style face="normal" font="default" size="100%">Barahona, Pedro</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">About infeasibility in the constraints of a linear model</style></title><secondary-title><style face="normal" font="default" size="100%">Ricerca Operativa</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1999</style></year></dates><publisher><style face="normal" font="default" size="100%">AIRO</style></publisher><volume><style face="normal" font="default" size="100%">92</style></volume><pages><style face="normal" font="default" size="100%">49-67</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, P.</style></author><author><style face="normal" font="default" size="100%">P. Barahona</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">After infeasibility in linear programming</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of CP-AI-OR99 workshop on integration of AI and OR techniques in Constraint Programming for Combinatorial Optimization problems</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1999</style></year></dates><publisher><style face="normal" font="default" size="100%">Universit</style></publisher><volume><style face="normal" font="default" size="100%">1</style></volume><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This work is focused on the correction of Infeasible Linear problems. Its motivation is not difficult to understand if one thinks on the complexity of model building in large real problems. The inconsistency can arise in the definition of the model due, for instance, to structural or data type errors. The identification of conflict sets of constraints is very useful but might not be enough to overcome the problem, since the implementation of a solution may require the definition of a new feasible model. We present a short review on known procedures for the diagnosis of these problems. The approach we propose is based on the correction of (potentially) all the parameters of the model restrictions. We present a pure algebraic methodology based on the Singular Value Decomposition of a matrix. This method is quite rigid in the changes of the matrix coefficients changes, so we give insights on a heuristic based approach in order to attain more flexibility.&lt;/p&gt;
</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Amaral, Paula</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">O algoritmo dos k-Caminhos mais curtos na relaxação do espaço de estados</style></title><secondary-title><style face="normal" font="default" size="100%">MsC Disertation, Faculty of Science, UL, Lisbon, Portugal (in Portuguese)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1993</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">n/a</style></abstract><notes><style face="normal" font="default" size="100%">n/a</style></notes></record></records></xml>