On the convergence of a smoothed penalty algorithm for semi-infinite programming

Qian Liu (), Changyu Wang and Xinmin Yang

Mathematical Methods of Operations Research, 2013, vol. 78, issue 2, 203-220

Abstract: For semi-infinite programming (SIP), we consider a class of smoothed penalty functions, which approximate the exact $$l_\rho (0>\rho \le 1)$$ penalty functions. On base of the smoothed penalty function, we present a feasible penalty algorithm for solving SIP. Without any boundedness condition or coercive condition, we establish the global convergence theorem. Then we present a perturbation theorem for this algorithm and obtain a necessary and sufficient condition for the convergence to the optimal value of SIP. Under Mangasarian–Fromovitz constrained qualification condition, we further discuss the convergence properties for the algorithm based upon a subclass of smooth approximations to the exact $$l_\rho $$ penalty function. Finally, numerical results are given. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Semi-infinite programming; Penalty algorithm; Global convergence; $$l_\rho $$ exact penalty function; Smooth approximation (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00186-013-0440-y

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