On merit functions for p-order cone complementarity problem

Xin He Miao; Yu Lin Chang; Jein Shan Chen

doi:10.1007/s10589-016-9889-y

On merit functions for p-order cone complementarity problem

Xin He Miao, Yu Lin Chang, Jein Shan Chen^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.

Original language	English
Pages (from-to)	155-173
Number of pages	19
Journal	Computational Optimization and Applications
Volume	67
Issue number	1
DOIs	https://doi.org/10.1007/s10589-016-9889-y
Publication status	Published - 2017 May 1

Keywords

Error bound
Merit function
p-order cone complementarity problem

ASJC Scopus subject areas

Control and Optimization
Computational Mathematics
Applied Mathematics

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10.1007/s10589-016-9889-y

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abstract = "Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.",

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T1 - On merit functions for p-order cone complementarity problem

AU - Miao, Xin He

AU - Chang, Yu Lin

AU - Chen, Jein Shan

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AB - Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.

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On merit functions for p-order cone complementarity problem

Abstract

Keywords

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