An interior-point method for MPECs based on strictly feasible relaxations

An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primal-dual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation … Read more

Combinatorial Structures in Nonlinear Programming

Non-smoothness and non-convexity in optimization problems often arise because a combinatorial structure is imposed on smooth or convex data. The combinatorial aspect can be explicit, e.g. through the use of ”max”, ”min”, or ”if” statements in a model, or implicit as in the case of bilevel optimization where the combinatorial structure arises from the possible … Read more

Local convergence of SQP methods for Mathematical Programs with Equilibrium Constraints

Recently, it has been shown that Nonlinear Programming solvers can successfully solve a range of Mathematical Programs with Equilibrium Constraints (MPECs). In particular, Sequential Quadratic Programming (SQP) methods have been very successful. This paper examines the local convergence properties of SQP methods applied to MPECs. It is shown that SQP converges superlinearly under reasonable assumptions … Read more