Publications

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A
Vieira, Manuel V. C. "The Accuracy of Interior-Point Methods Based on Kernel Functions." J. Optimization Theory and Applications. 155.2 (2012): 637-649. Abstract

For the last decade, interior-point methods that use barrier functions induced by some real univariate kernel functions have been studied. In these interior-point methods, the algorithm stops when a solution is found such that it is close (in the barrier function sense) to a point in the central path with the desired accuracy. However, this does not directly imply that the algorithm generates a solution with prescribed accuracy. Until now, this had not been appropriately addressed. In this paper, we analyze the accuracy of the solution produced by the aforementioned algorithm.

D
Vieira, Manuel V. C. "Derivatives of eigenvalues and Jordan frames." Numerical Algebra, Control and Optimization. 6.2 (2016): 115-126.
I
Anjos, Miguel F., and Manuel V. C. Vieira. "An improved two-stage optimization-based framework for unequal-areas facility layout." Optimization Letters. 10.7 (2016): 1379-1392.
Vieira, Manuel V. C. "Interior-point methods based on kernel functions for symmetric optimization." Optimization Methods and Software. 27.3 (2012): 513-537. Abstract

We present a generalization to symmetric optimization of interior-point methods for linear optimization based on kernel functions. Symmetric optimization covers the three most common conic optimization problems: linear, second-order cone and semi-definite optimization problems. Namely, we adapt the interior-point algorithm described in Peng et al. [Self-regularity: A New Paradigm for Primal–Dual Interior-point Algorithms. Princeton University Press, Princeton, NJ, 2002.] for linear optimization to symmetric optimization. The analysis is performed through Euclidean Jordan algebraic tools and a complexity bound is derived.

Vieira, Manuel V. C. "Interior-point methods for symmetric optimization based on a class of non-coercive kernel functions." Optimization Methods and Software. 28.3 (2013): 581-599.
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Jordan Algebraic Approach to Symmetric Optimization. Delft University of Technology. Delft, The Netherlands, 2007.PhD_vieira.pdf
M
Anjos, Miguel F., and Manuel V. C. Vieira. "Mathematical Optimization Approaches for Facility Layout Problems: The State-of-the-Art and Future Research Directions." European Journal of Operational Research. 261.1 (2017): 1-16.
O
Anjos, Miguel F., and Manuel V. C. Vieira. "On semidefinite least squares and minimal unsatisfiability." Discrete Applied Mathematics. 217 (2017): 79-96.
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Anjos, Miguel F., and Manuel V. C. Vieira. "Semidefinite Resolution and Exactness of Semidefinite Relaxations for Satisfiability." Discrete Applied Mathematics. 161.18 (2013): 2812-2826.