Convergence Analysis of a Trust-Region Multidimensional Filter Method for Nonlinear Complementarity Problems

A Trust Region Filter Method for Minimax Problems

In this paper, we propose a trust region filter method for minimax problems. Based on the filter technique, the minimax problem is transformed to a constrained optimization problem and solved by the traditional filter idea. In the presented algorithm, the acceptable criterion of the trial points is relaxed, so compared to the existed SQP and Newton-type methods for minimax method, this method i...

Projected filter trust region methods for a semismooth least squares formulation of mixed complementarity problems

A reformulation of the mixed complementarity problem as a box constrained overdetermined system of semismooth equations or, equivalently, a box constrained nonlinear least squares problem with zero residual is presented. Based on this reformulation, a trust region method for the solution of mixed complementarity problems is considered. This trust region method contains elements from different a...

Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming

A trust-region SQP-filter algorithm of the type introduced by Fletcher and Leyffer [Math. Program., 91 (2002), pp. 239–269] that decomposes the step into its normal and tangential components allows for an approximate solution of the quadratic subproblem and incorporates the safeguarding tests described in Fletcher, Leyffer, and Toint [On the Global Convergence of an SLPFilter Algorithm, Technic...

Global Convergence of a Hybrid Trust-Region SQP-Filter Algorithm for General Nonlinear Programming

A Trust Region Algorithm for Solving Nonlinear Equations (RESEARCH NOTE)

This paper presents a practical and efficient method to solve large-scale nonlinear equations. The global convergence of this new trust region algorithm is verified. The algorithm is then used to solve the nonlinear equations arising in an Expanded Lagrangian Function (ELF). Numerical results for the implementation of some large-scale problems indicate that the algorithm is efficient for these ...