Interior Methods for Mathematical Programs with Complementarity Constraints

Interior Methods for Mathematical Programs with Complementarity Constraints

This paper studies theoretical and practical properties of interior-penalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These re...

An ` 1 Elastic Interior - Point Methods for Mathematical Programs with Complementarity Constraints

We propose an interior-point algorithm based on an elastic formulation of the `1-penalty merit function for mathematical programs with complementarity constraints. The method generalizes that of Gould, Orban, and Toint (2003) and naturally converges to a strongly stationary point or delivers a certificate of degeneracy without recourse to second-order intermediate solutions. Remarkably, the met...

Smooth SQP Methods for Mathematical Programs with Nonlinear Complementarity Constraints

Mathematical programs with nonlinear complementarity constraints are refor-mulated using better-posed but nonsmooth constraints. We introduce a class offunctions, parameterized by a real scalar, to approximate these nonsmooth prob-lems by smooth nonlinear programs. This smoothing procedure has the extrabenefits that it often improves the prospect of feasibility and stability...

Mathematical Programs with Complementarity Constraints: Theory, Methods, and Applications

An 1 Elastic Interior-Point Method for Mathematical Programs with Complementarity Constraints

We propose an interior-point algorithm based on an elastic formulation of the `1penalty merit function for mathematical programs with complementarity constraints. The salient feature of our method is that it requires no prior knowledge of which constraints, if any, are complementarity constraints. Remarkably, the method allows for a unified treatment of both general, unstructured, degenerate pr...