On solving a class of linear semi-infinite programming by SDP method

Yi Xu; Wenyu Sun; Liqun Qi

doi:10.1080/02331934.2013.793325

On solving a class of linear semi-infinite programming by SDP method

Yi Xu, Wenyu Sun, Liqun Qi

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

12 Citations (Scopus)

Abstract

In this paper, we present a new method to solve linear semi-infinite programming. This method bases on the fact that the nonnegative polynomial on (Formula presented.) could be turned into a positive semi-definite system, so we can use the nonnegative polynomials to approximate the semi-infinite constraint. Furthermore, we set up an approximate programming for the primal linear semi-infinite programming, and obtain an error bound between two programming problems. Numerical results show that our method is efficient.

Original language	English
Pages (from-to)	603-616
Number of pages	14
Journal	Optimization
Volume	64
Issue number	3
DOIs	https://doi.org/10.1080/02331934.2013.793325
Publication status	Published - 1 Jan 2015

Keywords

error bound
nonnegative polynomial
semi-definite programming
semi-infinite programming
SOS method

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1080/02331934.2013.793325

Cite this

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N2 - In this paper, we present a new method to solve linear semi-infinite programming. This method bases on the fact that the nonnegative polynomial on (Formula presented.) could be turned into a positive semi-definite system, so we can use the nonnegative polynomials to approximate the semi-infinite constraint. Furthermore, we set up an approximate programming for the primal linear semi-infinite programming, and obtain an error bound between two programming problems. Numerical results show that our method is efficient.

AB - In this paper, we present a new method to solve linear semi-infinite programming. This method bases on the fact that the nonnegative polynomial on (Formula presented.) could be turned into a positive semi-definite system, so we can use the nonnegative polynomials to approximate the semi-infinite constraint. Furthermore, we set up an approximate programming for the primal linear semi-infinite programming, and obtain an error bound between two programming problems. Numerical results show that our method is efficient.

KW - error bound

KW - nonnegative polynomial

KW - semi-definite programming

KW - semi-infinite programming

KW - SOS method

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On solving a class of linear semi-infinite programming by SDP method

Abstract

Keywords

ASJC Scopus subject areas

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