Tawhid, M. An unconstrained optimization technique for nonsmooth nonlinear complementarity problems. (English) Zbl 1203.90161 JIPAM, J. Inequal. Pure Appl. Math. 10, No. 3, Paper No. 68, 14 p. (2009). 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 Keywords:nonlinear complementarity problem; unconstrained minimization; NCP function; merit function; regularity conditions; nonsmooth function; descent algorithm PDFBibTeX XMLCite \textit{M. Tawhid}, JIPAM, J. Inequal. Pure Appl. Math. 10, No. 3, Paper No. 68, 14 p. (2009; Zbl 1203.90161) Full Text: EuDML EMIS