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

Authors:
Liqun Qi;Chen Ling;Xiaojiao Tong;Guanglu Zhou
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, China 310018;Institute of Mathematics, Changsha University of Science and Technology, Changsha, China;Department of Mathematics and Statistics, Curtin University of Technology, Bentley, Australia
Venue:
Computational Optimization and Applications
Year:
2009

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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.