We present a theorem of Sard type for semi-algebraic set-valued mappings whose graphs have dimension no larger than that of their range space: the inverse of such a mapping admits a single-valued analytic localization around any pair in the graph, for a generic value parameter. This simple result yields a transparent and unified treatment of generic properties of semi-algebraic optimization pro...

February 7, 1996 (Revised June 25, 1996) Abstract. Recently, Luo and Tseng proposed a class of merit functions for the nonlinear complementarity problem (NCP) and showed that it enjoys several interesting properties under some assumptions. In this paper, adopting a similar idea to Luo and Tseng's, we present new merit functions for the NCP, which can be decomposed into component functions. We s...

In this paper, we study several NCP-functions for the nonlinear complementarity problem (NCP) which are indeed based on the generalized Fischer-Burmeister function, φp(a, b) = ‖(a, b)‖p−(a+b). It is well known that the NCP can be reformulated as an equivalent unconstrained minimization by means of merit functions involving NCPfunctions. Thus, we aim to investigate some important properties of t...

The modeling of migration of hydrogen produced by the corrosion of the nuclear waste packages in an underground storage including the dissolution of hydrogen involves a set of nonlinear partial differential equations with nonlinear complementarity constraints. This article shows how to apply a modern and efficient solution strategy, the Newton-min method, to this geoscience problem and investig...

We propose a generalized Newton method for solving the system of nonlinear equations with linear complementarity constraints in the implicit or semi-implicit time-stepping scheme for differential linear complementarity systems (DLCS). We choose a specific solution from the solution set of the linear complementarity constraints to define a locally Lipschitz continuous right-hand-side function in...

We establish a discrete multivariate mean value theorem for the class of positive maximum component sign preserving functions. A constructive and combinatorial proof is given based upon a simplicial algorithm and vector labeling. Moreover, we apply this theorem to a discrete nonlinear complementarity problem and an economic equilibrium problem with indivisibilities and show the existence of sol...

We consider a regularization proximal method with variable metric to solve the nonlinear complementarity problem (NCP ) for P0functions. We establish global convergence properties when the solution set is non empty and bounded. Furthermore, we prove, without boundedness of the solution set, that the sequence generated by the algorithm is a minimizing sequence for the implicit Lagrangian functio...

The symmetric cone complementarity problem (denoted by SCCP) is a class of equilibrium optimization problems, and it contains the standard linear/nonlinear complementarity problem (LCP/NCP), the second-order cone complementarity problem (SOCCP) and the semidefinite complementarity problem (SDCP) as special cases. In this paper, we present a regularized smoothing Newton algorithm for SCCP by mak...