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An unconstrained optimization technique for nonsmooth nonlinear complementarity problems. (English) Zbl 1203.90161

Summary: We consider an unconstrained minimization formulation of the nonlinear complementarity problem NCP\( (f)\) when the underlying functions are \( H\)-differentiable but not necessarily locally Lipschitzian or directionally differentiable. We show how, under appropriate regularity conditions on an \( H\)-differential of \( f\), minimizing the merit function corresponding to \( f\) leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for \( C^1\)-functions, semismooth-functions, and for locally Lipschitzian functions. We also show a result on the global convergence of a derivative-free descent algorithm for solving nonsmooth nonlinear complementarity problem.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C20 Quadratic programming
90C56 Derivative-free methods and methods using generalized derivatives
49J52 Nonsmooth analysis
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