Volume 22, Issue 3
A Truly Globally Convergent Feasible Newton-Type Method for Mixed Complementarity Problems

Deren Han

DOI:

J. Comp. Math., 22 (2004), pp. 347-360

Published online: 2004-06

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  • Abstract

Typical solution methods for solving mixed complementarity problems either generate feasible iterates but have to solve relatively complicated subproblems such as quadratic programs or linear complementarity problems, or (those methods) have relatively simple subproblems such as system of linear equations but possibly generate infeasible iterates. In this paper, we propose a new Newton-type method for solving monotone mixed com- plementarity problems, which ensures to generate feasible iterates, and only has to solve a system of well-conditioned linear equations with reduced dimension per iteration. Without any regularity assumption, we prove that the whole sequence of iterates converges to a so- lution of the problem (truly globally convergent). Furthermore, under suitable conditions, the local superlinear rate of convergence is also established.

  • Keywords

Mixed complementarity problems Newton-type methods Global convergence Superlinear convergence

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@Article{JCM-22-347, author = {}, title = {A Truly Globally Convergent Feasible Newton-Type Method for Mixed Complementarity Problems}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {3}, pages = {347--360}, abstract = { Typical solution methods for solving mixed complementarity problems either generate feasible iterates but have to solve relatively complicated subproblems such as quadratic programs or linear complementarity problems, or (those methods) have relatively simple subproblems such as system of linear equations but possibly generate infeasible iterates. In this paper, we propose a new Newton-type method for solving monotone mixed com- plementarity problems, which ensures to generate feasible iterates, and only has to solve a system of well-conditioned linear equations with reduced dimension per iteration. Without any regularity assumption, we prove that the whole sequence of iterates converges to a so- lution of the problem (truly globally convergent). Furthermore, under suitable conditions, the local superlinear rate of convergence is also established. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8855.html} }
TY - JOUR T1 - A Truly Globally Convergent Feasible Newton-Type Method for Mixed Complementarity Problems JO - Journal of Computational Mathematics VL - 3 SP - 347 EP - 360 PY - 2004 DA - 2004/06 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8855.html KW - Mixed complementarity problems KW - Newton-type methods KW - Global convergence KW - Superlinear convergence AB - Typical solution methods for solving mixed complementarity problems either generate feasible iterates but have to solve relatively complicated subproblems such as quadratic programs or linear complementarity problems, or (those methods) have relatively simple subproblems such as system of linear equations but possibly generate infeasible iterates. In this paper, we propose a new Newton-type method for solving monotone mixed com- plementarity problems, which ensures to generate feasible iterates, and only has to solve a system of well-conditioned linear equations with reduced dimension per iteration. Without any regularity assumption, we prove that the whole sequence of iterates converges to a so- lution of the problem (truly globally convergent). Furthermore, under suitable conditions, the local superlinear rate of convergence is also established.
Deren Han . (1970). A Truly Globally Convergent Feasible Newton-Type Method for Mixed Complementarity Problems. Journal of Computational Mathematics. 22 (3). 347-360. doi:
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