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arXiv · 2009.14047

Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints

Christian Kirches·Jeffrey Larson·Sven Leyffer·Paul Manns
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Abstract

We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to obtain an estimate of the active set. The algorithm enforces descent on the objective function to promote global convergence to B-stationary points. We provide a convergence analysis and preliminary numerical results on a range of test problems. We also study the effect of fixing the active constraints in a bound-constrained quadratic program that can be solved on each iteration in order to obtain fast convergence.

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Christian Kirches, Jeffrey Larson, Sven Leyffer, Paul Manns. 2020-09-29. Sequential Linearization Method for Bound-Constrained Mathematical Programs with Complementarity Constraints. https://doi.org/10.1137/20m1370501

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