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A new regularization scheme for mathematical programs with complementarity constraints. (English) Zbl 1187.65064

The authors present a regularization scheme for mathematical programs with complementarity constraints where the complementarity system is relaxed to inequalities. The proposed regularization does not assume any second-order condition to ensure the existence of the regularized stationary points. The standard linear independence constraint qualifications are shown to hold for this regularization except some particular points. The existence of the Lagrange multipliers is shown for every feasible point of the regularized problem. The authors prove that the regularized problems possess Karush-Kuhn-Tucker multipliers, and regularized solutions are shown to converge strongly stationary points under certain assumptions. Some numerical experimental results are presented to confirm the convergence results.

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

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