A smoothing projected Newton-type algorithm for semi-infinite programming

Liqun Qi; Chen Ling; Xiaojiao Tong; Guanglu Zhou

doi:10.1007/s10589-007-9117-x

A smoothing projected Newton-type algorithm for semi-infinite programming

Liqun Qi, Chen Ling, Xiaojiao Tong, Guanglu Zhou

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

24 Citations (Scopus)

Abstract

This paper presents a smoothing projected Newton-type method for solving the semi-infinite programming (SIP) problem. We first reformulate the KKT system of the SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing projected Newton-type algorithm. At each iteration only a system of linear equations needs to be solved. The feasibility is ensured via the aggregated constraint under some conditions. Global and local superlinear convergence of this method is established under some standard assumptions. Preliminary numerical results are reported.

Original language	English
Pages (from-to)	1-30
Number of pages	30
Journal	Computational Optimization and Applications
Volume	42
Issue number	1
DOIs	https://doi.org/10.1007/s10589-007-9117-x
Publication status	Published - 1 Jan 2009

Keywords

Constrained equations
Convergence
KKT system
Semi-infinite programming
Smoothing method

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Control and Optimization

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10.1007/s10589-007-9117-x

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AB - This paper presents a smoothing projected Newton-type method for solving the semi-infinite programming (SIP) problem. We first reformulate the KKT system of the SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing projected Newton-type algorithm. At each iteration only a system of linear equations needs to be solved. The feasibility is ensured via the aggregated constraint under some conditions. Global and local superlinear convergence of this method is established under some standard assumptions. Preliminary numerical results are reported.

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KW - Semi-infinite programming

KW - Smoothing method

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A smoothing projected Newton-type algorithm for semi-infinite programming

Abstract

Keywords

ASJC Scopus subject areas

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