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Mathematical analysis demonstrates superlinear local convergence of sequential quadratic programming for equilibrium-constrained programs, highlighting the necessity of key stationarity assumptions.
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.
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Fletcher et al. (2006) studied this question.
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