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

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 ca...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2006-04, Vol.129 (1), p.147-164
Main Authors: LING, C, QI, L. Q, ZHOU, G. L, WU, S. Y
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Applied sciences
Approximation
Convergence
Exact sciences and technology
Integrals
Mathematical analysis
Mathematical functions
Mathematical models
Methods
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Programming
Smoothing
Studies
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Summary: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 algorithm, 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. [PUBLICATION ABSTRACT]
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-006-9049-0