<?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%">Vicente da Silva, M.</style></author><author><style face="normal" font="default" size="100%">N. Deusdado</style></author><author><style face="normal" font="default" size="100%">Antão, A. N.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Lower and upper bound limit analysis via the alternating direction method of multipliers</style></title><secondary-title><style face="normal" font="default" size="100%">Computers and Geotechnics</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Alternating direction method of multipliers</style></keyword><keyword><style  face="normal" font="default" size="100%">augmented Lagrangian</style></keyword><keyword><style  face="normal" font="default" size="100%">limit analysis</style></keyword><keyword><style  face="normal" font="default" size="100%">Lower bound</style></keyword><keyword><style  face="normal" font="default" size="100%">Nonsmooth optimization</style></keyword><keyword><style  face="normal" font="default" size="100%">Upper bound</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/pii/S0266352X20301348</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">124</style></volume><pages><style face="normal" font="default" size="100%">103571</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Computational limit analysis methods invariably lead to the need to solve a mathematical programming problem. The alternating direction method of multipliers (ADMM) is one versatile and robust technique to solve non-linear convex optimization problems that has recently found applications in a wide range of fields. Its solution scheme, based on an operator splitting algorithm, is not only easy to implement but also suitable to efficiently solve large-scale variational problems. Starting from the ADMM framework, we derive a strict upper bound finite element formulation using a two-(primal)-field approximation, one for the velocity field and the other for the plastic strain rate field. Next, following a similar approach, we develop a novel strict lower bound formulation. Here, the two-(primal)-field model is based on a redundant approximation of the stress field. Duality principles are then explored in order to unify these two formulations.The effectiveness of this approach is demonstrated on test problems and, to conclude, some considerations are made about the performance results.&lt;/p&gt;
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