Polak, E.; Mayne, D. Q.; Higgins, J. E. On the extension of Newton’s method to semi-infinite minimax problems. (English) Zbl 0756.90088 SIAM J. Control Optim. 30, No. 2, 367-389 (1992). The authors introduce two new techniques for the analysis and construction of semi-infinite optimization algorithms. The first technique is designed for the superlinear rate of convergence of semi-infinite optimization routines. The second technique enables specification of discretization rules that preserve the superlinear convergence of conceptual, superlinearly converging semi-infinite optimization algorithms. Natural extensions of Newton’s method to semi-infinite optimization are used for presenting the techniques. In particular, it is shown that both local and global versions of the conceptual extension of Newton’s method converge \(Q\)-superlinearly, with rate at least 3/2, and that their implementations based on discretization rules, retain this rate of convergence. Reviewer: Alexander Shapiro (Pretoria) Cited in 12 Documents MSC: 90C34 Semi-infinite programming 49K35 Optimality conditions for minimax problems 49M15 Newton-type methods Keywords:semi-infinite optimization; superlinear rate of convergence; Newton’s method PDFBibTeX XMLCite \textit{E. Polak} et al., SIAM J. Control Optim. 30, No. 2, 367--389 (1992; Zbl 0756.90088) Full Text: DOI