Local convergence of SQP methods for Mathematical Programs with Equilibrium Constraints

Roger Fletcher (fletchermaths.dundee.ac.uk)
Sven Leyffer (sleyffermaths.dundee.ac.uk)
Danny Ralph (d.ralphjims.cam.ac.uk)
Stefan Scholtes (s.scholtesjims.cam.ac.uk)

Abstract: 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 near a strongly stationary point. A number of illustrative examples are presented which show that some of the assumptions are difficult to relax.

Keywords: Nonlinear programming, SQP, MPEC, MPCC, equilibrium constraints

Category 1: Complementarity and Variational Inequalities

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Numerical Analysis Report NA/209, Department of Mathematics, University of Dundee, May 2002.

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Entry Submitted: 05/09/2002
Entry Accepted: 05/09/2002
Entry Last Modified: 05/29/2002

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