Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming |
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| Authors: | C Ling L Q Qi G L Zhou S Y Wu |
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| Institution: | (1) School of Information, Zhejiang University of Finance and Economics, Hangzhou, China;(2) Department of Mathematics, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong;(3) Department of Mathematics and Statistics, Curtin University of Technology, Bentley, Western Australia, Australia;(4) Institute of Applied Mathematics, National Cheng-Kung University, Tainan, Taiwan |
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| 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.
Communicated by F. Giannessi
His work was supported by the Hong Kong Research Grant Council
His work was supported by the Australian Research Council. |
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| Keywords: | Smoothing SQP algorithm semi-infinite programming integral functions global convergence |
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