Abstract
For the semi-infinite programming (SIP) problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.
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This research is supported by the National Natural Science Foundation of China under Grant Nos. 10971118, 10701047 and 10901096, and the Natural Science Foundation of Shandong Province under Grant Nos. ZR2009AL019 and BS2010SF010.
This paper was recommended for publication by Editor Shouyang WANG.
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Wang, C., Zhang, H. & Liu, F. Global convergence of a class of smooth penalty methods for semi-infinite programming. J Syst Sci Complex 24, 769–783 (2011). https://doi.org/10.1007/s11424-011-8427-3
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DOI: https://doi.org/10.1007/s11424-011-8427-3