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An interior point method for mathematical programs with complementarity constraints (MPCCs). (English) Zbl 1077.90079

Summary: Interior point methods for nonlinear programs (NLPs) are adapted for solution of mathematical programs with complementarity constraints (MPCCs). The constraints of the MPCC are suitably relaxed so as to guarantee a strictly feasible interior for the inequality constraints. The standard primal-dual algorithm has been adapted with a modified step calculation. The algorithm is shown to be superlinearly convergent in the neighborhood of the solution set under assumptions of MPCC-LICQ, strong stationarity and upper level strict complementarity. The modification can be easily accommodated within most nonlinear programming interior point algorithms with identical local behavior. Numerical experience is also presented and holds promise for the proposed method.

MSC:

90C51 Interior-point methods
90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
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