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An SQP method for mathematical programs with complementarity constraints with strong convergence properties. (English) Zbl 1357.49124

Summary: We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterates generated by our SQP method are at least M-stationary.

MSC:

49M37 Numerical methods based on nonlinear programming
90C26 Nonconvex programming, global optimization
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C55 Methods of successive quadratic programming type

Software:

MacMPEC; AMPL; Matlab
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