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

Authors:
Chen Ling;Qin Ni;Liqun Qi;Soon-Yi Wu
Affiliations:
School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, China 310018 and Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Ko ...;Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, China 210016;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Mathematics, National Cheng Kung University/National Center for Theoretical Sciences, Tainan, Taiwan
Venue:
Journal of Global Optimization
Year:
2010

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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.