Lagrangian globalization methods for nonlinear complementarity problems

Xiaojun Chen; Liqun Qi; Y. F. Yang

doi:10.1023/A:1013092412197

Lagrangian globalization methods for nonlinear complementarity problems

Xiaojun Chen
, Liqun Qi
, Y. F. Yang

Research output: Journal article publication › Journal article › Academic research › peer-review

13 Citations (Scopus)

Abstract

This paper extends the Lagrangian globalization (LG) method to the nonsmooth equation Φ(x)=0 arising from a nonlinear complementarity problem (NCP) and presents a descent algorithm for the LG phase. The aim of this paper is not to present a new method for solving the NCP, but to find x̂ such that ∥Φ(x̂)∥ < ∥Φ(x̄)∥ when the NCP has a solution and x̄ is a stationary point but not a solution.

Original language	English
Pages (from-to)	77-95
Number of pages	19
Journal	Journal of Optimization Theory and Applications
Volume	112
Issue number	1
DOIs	https://doi.org/10.1023/A:1013092412197
Publication status	Published - 1 Jan 2002

Keywords

descent methods
global convergence
Lagrangians
Nonlinear complementarity problems
nonsmooth equations

ASJC Scopus subject areas

Applied Mathematics
Control and Optimization
Management Science and Operations Research

More information

10.1023/A:1013092412197

Cite this

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abstract = "This paper extends the Lagrangian globalization (LG) method to the nonsmooth equation Φ(x)=0 arising from a nonlinear complementarity problem (NCP) and presents a descent algorithm for the LG phase. The aim of this paper is not to present a new method for solving the NCP, but to find {\^x} such that ∥Φ({\^x})∥ < ∥Φ({\=x})∥ when the NCP has a solution and {\=x} is a stationary point but not a solution.",

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AU - Yang, Y. F.

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AB - This paper extends the Lagrangian globalization (LG) method to the nonsmooth equation Φ(x)=0 arising from a nonlinear complementarity problem (NCP) and presents a descent algorithm for the LG phase. The aim of this paper is not to present a new method for solving the NCP, but to find x̂ such that ∥Φ(x̂)∥ < ∥Φ(x̄)∥ when the NCP has a solution and x̄ is a stationary point but not a solution.

KW - descent methods

KW - global convergence

KW - Lagrangians

KW - Nonlinear complementarity problems

KW - nonsmooth equations

UR - https://www.scopus.com/pages/publications/0036111268

U2 - 10.1023/A:1013092412197

DO - 10.1023/A:1013092412197

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JF - Journal of Optimization Theory and Applications

IS - 1

ER -

Lagrangian globalization methods for nonlinear complementarity problems

Abstract

Keywords

ASJC Scopus subject areas

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