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.
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Chen Ling work was supported by the National Natural Science Foundation of China (10871168), the Zhejiang Provincial National Science Foundation of China (Y606168) and a Hong Kong Polytechnic University Postdoctoral Fellowship. Qin Ni work was supported by the National Natural Science Foundation of China (grant 10471062). Liqun Qi work was supported by the Hong Kong Research Grant Council (Grant PolyU 102307) and a Chair Professor Fund of the Hong Kong Polytechnic University.
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Ling, C., Ni, Q., Qi, L. et al. A new smoothing Newton-type algorithm for semi-infinite programming. J Glob Optim 47, 133–159 (2010). https://doi.org/10.1007/s10898-009-9462-7
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DOI: https://doi.org/10.1007/s10898-009-9462-7