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

Chen Ling; Qin Ni; Liqun Qi; Soon Yi Wu

doi:10.1007/s10898-009-9462-7

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

Chen Ling, Qin Ni, Liqun Qi, Soon Yi Wu

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

17 Citations (Scopus)

Abstract

We consider a semismooth reformulation of the KKT system arising from the semi-infinite programming (SIP) problem. Based upon this reformulation, we present a new smoothing Newton-type method for the solution of SIP problem. The main properties of this method are: (a) it is globally convergent at least to a stationary point of the SIP problem, (b) it is locally superlinearly convergent under a certain regularity condition, (c) the feasibility is ensured via the aggregated constraint, and (d) it has to solve just one linear system of equations at each iteration. Preliminary numerical results are reported. 2009.

Original language	English
Pages (from-to)	133-159
Number of pages	27
Journal	Journal of Global Optimization
Volume	47
Issue number	1
DOIs	https://doi.org/10.1007/s10898-009-9462-7
Publication status	Published - 1 May 2010

Keywords

Convergence
KKT system
Nonsmooth equations
Semi-infinite programming (SIP) problem
Smoothing method

ASJC Scopus subject areas

Computer Science Applications
Control and Optimization
Applied Mathematics
Management Science and Operations Research

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10.1007/s10898-009-9462-7

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abstract = "We consider a semismooth reformulation of the KKT system arising from the semi-infinite programming (SIP) problem. Based upon this reformulation, we present a new smoothing Newton-type method for the solution of SIP problem. The main properties of this method are: (a) it is globally convergent at least to a stationary point of the SIP problem, (b) it is locally superlinearly convergent under a certain regularity condition, (c) the feasibility is ensured via the aggregated constraint, and (d) it has to solve just one linear system of equations at each iteration. Preliminary numerical results are reported. 2009.",

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AU - Ling, Chen

AU - Ni, Qin

AU - Qi, Liqun

AU - Wu, Soon Yi

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N2 - We consider a semismooth reformulation of the KKT system arising from the semi-infinite programming (SIP) problem. Based upon this reformulation, we present a new smoothing Newton-type method for the solution of SIP problem. The main properties of this method are: (a) it is globally convergent at least to a stationary point of the SIP problem, (b) it is locally superlinearly convergent under a certain regularity condition, (c) the feasibility is ensured via the aggregated constraint, and (d) it has to solve just one linear system of equations at each iteration. Preliminary numerical results are reported. 2009.

AB - We consider a semismooth reformulation of the KKT system arising from the semi-infinite programming (SIP) problem. Based upon this reformulation, we present a new smoothing Newton-type method for the solution of SIP problem. The main properties of this method are: (a) it is globally convergent at least to a stationary point of the SIP problem, (b) it is locally superlinearly convergent under a certain regularity condition, (c) the feasibility is ensured via the aggregated constraint, and (d) it has to solve just one linear system of equations at each iteration. Preliminary numerical results are reported. 2009.

KW - Convergence

KW - KKT system

KW - Nonsmooth equations

KW - Semi-infinite programming (SIP) problem

KW - Smoothing method

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SP - 133

EP - 159

JO - Journal of Global Optimization

JF - Journal of Global Optimization

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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