Fletcher, Roger; Leyffer, Sven; Ralph, Danny; Scholtes, Stefan Local convergence of SQP methods for mathematical programs with equilibrium constraints. (English) Zbl 1112.90098 SIAM J. Optim. 17, No. 1, 259-286 (2006). Summary: Recently, nonlinear programming solvers have been used to 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. SQP is shown to converge superlinearly under reasonable assumptions near a strongly stationary point. A number of examples are presented that show that some of the assumptions are difficult to relax. Cited in 2 ReviewsCited in 92 Documents MSC: 90C55 Methods of successive quadratic programming type 90C30 Nonlinear programming 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 65K05 Numerical mathematical programming methods Keywords:nonlinear programming; sequential quadratic programming (SQP); mathematical programs with equilibrium constraints (MPEC); mathematical programs with complementarity constraints (MPCC); equilibrium constraints Software:MacMPEC; LANCELOT PDFBibTeX XMLCite \textit{R. Fletcher} et al., SIAM J. Optim. 17, No. 1, 259--286 (2006; Zbl 1112.90098) Full Text: DOI