On the Parametric Nonlinear Complementarity Problem
نویسنده
چکیده
A parametrized version of the nonlinear complementarity problem is formulated. The existence of a continuation of a solution is investigated and sufficient and necessary conditions for the monotonicity of such a continuation are given. The notions of strong and uniform monotonicity, originated in the linear theory, are discussed, and the theorems of the linear theory are generalized.
منابع مشابه
An interior-point algorithm for $P_{ast}(kappa)$-linear complementarity problem based on a new trigonometric kernel function
In this paper, an interior-point algorithm for $P_{ast}(kappa)$-Linear Complementarity Problem (LCP) based on a new parametric trigonometric kernel function is proposed. By applying strictly feasible starting point condition and using some simple analysis tools, we prove that our algorithm has $O((1+2kappa)sqrt{n} log nlogfrac{n}{epsilon})$ iteration bound for large-update methods, which coinc...
متن کاملA New Class of Semismooth Newton-Type Methods for Nonlinear Complementarity Problems
We introduce a new, one-parametric class of NCP-functions. This class subsumes the Fischer function and reduces to the minimum function in a limiting case of the parameter. This new class of NCP-functions is used in order to reformulate the nonlinear complementarity problem as a nonsmooth system of equations. We present a detailed investigation of the properties of the equation operator, of the...
متن کاملA class of smoothing functions for nonlinear and mixed complementarity problems
We propose a class of parametric smooth functions that approximate the fundamental plus function, (x) + =maxf0; xg, by twice integrating a probability density function. This leads to classes of smooth parametric nonlinear equation approximations of nonlinear and mixed complementarity problems (NCPs and MCPs). For any solvable NCP or MCP, existence of an arbitrarily accurate solution to the smoo...
متن کاملAn infeasible interior-point method for the $P*$-matrix linear complementarity problem based on a trigonometric kernel function with full-Newton step
An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...
متن کاملContinuation method for nonlinear complementarity problems via normal maps
In a recent paper by Chen and Mangasarian (C. Chen, O.L. Mangasarian, A class of smoothing functions for nonlinear and mixed complementarity problems, Computational Optimization and Applications 2 (1996), 97±138) a class of parametric smoothing functions has been proposed to approximate the plus function present in many optimization and complementarity related problems. This paper uses these sm...
متن کامل