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

For semi-infinite programming (SIP), we consider a class of smoothed penalty functions, which approximate the exact \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_\rho (0<\rho \le 1)$$\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_\rho $$\end{document} penalty function. Finally, numerical results are given.