A regularization method for the second-order cone complementarity problem with the Cartesian P0-property

Shaohua Pan, Jein Shan Chen

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We consider the Tikhonov regularization method for the second-order cone complementarity problem (SOCCP) with the Cartesian P0-property. We show that many results of the regularization method for the P0-nonlinear complementarity problem still hold for this important class of nonmonotone SOCCP. For example, under the more general setting, every regularized problem has the unique solution, and the solution trajectory generated is bounded if the original SOCCP has a nonempty and bounded solution set. We also propose an inexact regularization algorithm by solving the sequence of regularized problems approximately with the merit function approach based on Fischer-Burmeister merit function, and establish the convergence result of the algorithm. Preliminary numerical results are also reported, which verify the favorable theoretical properties of the proposed method.

Original languageEnglish
Pages (from-to)1475-1491
Number of pages17
JournalNonlinear Analysis, Theory, Methods and Applications
Volume70
Issue number4
DOIs
Publication statusPublished - 2009 Feb 15

Fingerprint

Second-order Cone
Complementarity Problem
Regularization Method
Cartesian
Cones
Merit Function
Nonlinear Complementarity Problem
Tikhonov Regularization
Bounded Solutions
Bounded Set
Solution Set
Unique Solution
Convergence Results
Regularization
Trajectories
Trajectory
Verify
Numerical Results

Keywords

  • Cartesian P-property
  • Fischer-Burmeister merit function
  • Second-order cone complementarity problem
  • Tikhonov regularization

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

A regularization method for the second-order cone complementarity problem with the Cartesian P0-property. / Pan, Shaohua; Chen, Jein Shan.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 70, No. 4, 15.02.2009, p. 1475-1491.

Research output: Contribution to journalArticle

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