Search

Abstract: The smoothing-type algorithm has been successfully applied to solve various optimization problems. In general, the smoothing-type algorithm is designed based on some monotone line search. However, in order to achieve better numerical results, the non-monotone line search technique has been used in the numerical computations of some smoothing-type algorithms. In this paper, we propose a smoothing-type algorithm for solving the nonlinear complementarity problem with a non-monotone line search. We show that the proposed algorithm is globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are also reported. [Copyright &y& Elsevier]

Abstract: Recently, filter methods are extensively studied to handle nonlinear programming problems. Because of good numerical results, filter techniques are attached importance to. The nonlinear complementarity problem can be reformulated as the least -norm solution of an optimization problem. In this paper, basing on the filter technique and the new smoothing function, we present a new Filter-Levenberg–Marquardt method for solving the equation system with the disturbance . Under the assumption that the lever set of the problem is compact, we prove its global convergence. [Copyright &y& Elsevier]

Abstract: In the paper [J.-S. Chen, S. Pan, A family of NCP-functions and a descent method for the nonlinear complementarity problem, Computational Optimization and Applications, 40 (2008) 389–404], the authors proposed a derivative-free descent algorithm for nonlinear complementarity problems (NCPs) by the generalized Fischer–Burmeister merit function: , and observed that the choice of the parameter has a great influence on the numerical performance of the algorithm. In this paper, we analyze the phenomenon theoretically for a derivative-free descent algorithm which is based on a penalized form of and uses a different direction from that of Chen and Pan. More specifically, we show that the algorithm proposed is globally convergent and has a locally -linear convergence rate, and furthermore, its convergence rate will become worse when the parameter decreases. Numerical results are also reported for the test problems from MCPLIB, which further verify the theoretical results obtained. [Copyright &y& Elsevier]

The smoothing-type algorithm has been a powerful tool for solving various optimization problems. In order to improve the numerical results of the algorithm, the nonmonotone line search technique has been used when the algorithm is implemented. However, the theoretical analysis is based on the algorithm with some monotone line search. In this paper, based on the smoothed Kanzow-Kleinmichel NCP function, we propose a smoothing Newton algorithm for solving the nonlinear complementarity problem with a new nonmonotone line search. We show that the nonmonotone algorithm is globally and locally superlinearly convergent under suitable assumptions. The preliminary numerical results are also reported. [ABSTRACT FROM AUTHOR]

Abstract: The nonlinear complementarity problem (denoted by NCP(F)) can be reformulated as the least l 2-norm solution of a optimization problem. By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions. Then a smoothing Levenberg–Marquardt method is applied to solve the parameterized optimization problems. The global convergence of the proposed method is proved under an assumption that the level set of the problem is compact. [Copyright &y& Elsevier]