Global convergence of a robust smoothing SQP method for semi-infinite programming

C. Ling; Liqun Qi; G. L. Zhou; S. Y. Wu

doi:10.1007/s10957-006-9049-0

Global convergence of a robust smoothing SQP method for semi-infinite programming

C. Ling, Liqun Qi, G. L. Zhou, S. Y. Wu

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

15 Citations (Scopus)

Abstract

The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the integral function, gradient-based algorithms cannot be used to solve this nonsmooth nonlinear programming problem. To overcome this difficulty, we present a robust smoothing sequential quadratic programming (SQP) algorithm for solving the nonsmooth nonlinear programming problem. At each iteration of the algorthm, we need to solve only a quadratic program that is always feasible and solvable. The global convergence of the algorithm is established under mild conditions. Numerical results are given.

Original language	English
Pages (from-to)	147-164
Number of pages	18
Journal	Journal of Optimization Theory and Applications
Volume	129
Issue number	1
DOIs	https://doi.org/10.1007/s10957-006-9049-0
Publication status	Published - 1 Apr 2006
Externally published	Yes

Keywords

Global convergence
Integral functions
Semi-infinite programming
Smoothing SQP algorithm

ASJC Scopus subject areas

Control and Optimization
Management Science and Operations Research
Applied Mathematics

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10.1007/s10957-006-9049-0

Cite this

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AU - Qi, Liqun

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AU - Wu, S. Y.

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AB - The semi-infinite programming (SIP) problem is a program with infinitely many constraints. It can be reformulated as a nonsmooth nonlinear programming problem with finite constraints by using an integral function. Due to the nondifferentiability of the integral function, gradient-based algorithms cannot be used to solve this nonsmooth nonlinear programming problem. To overcome this difficulty, we present a robust smoothing sequential quadratic programming (SQP) algorithm for solving the nonsmooth nonlinear programming problem. At each iteration of the algorthm, we need to solve only a quadratic program that is always feasible and solvable. The global convergence of the algorithm is established under mild conditions. Numerical results are given.

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Global convergence of a robust smoothing SQP method for semi-infinite programming

Abstract

Keywords

ASJC Scopus subject areas

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