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On the extension of Newton’s method to semi-infinite minimax problems. (English) Zbl 0756.90088

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.

MSC:

90C34 Semi-infinite programming
49K35 Optimality conditions for minimax problems
49M15 Newton-type methods
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