A smooth method for the finite minimax problem |
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Authors: | G. Di Pillo L. Grippo S. Lucidi |
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Affiliation: | (1) Dipartimento di Informatica e Sistemistica, Università di Roma La Sapienza, Via Buonarrota 12, 00185 Roma, Italy;(2) Istituto di Analisi dei Sistemi e Informatica del CNR, Roma, Italy |
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Abstract: | We consider unconstrained minimax problems where the objective function is the maximum of a finite number of smooth functions. We prove that, under usual assumptions, it is possible to construct a continuously differentiable function, whose minimizers yield the minimizers of the max function and the corresponding minimum values. On this basis, we can define implementable algorithms for the solution of the minimax problem, which are globally convergent at a superlinear convergence rate. Preliminary numerical results are reported.This research was partially supported by the National Research Program on Metodi di ottimizzazione per le decisioni, Ministero dell'Università e della Ricerca Scientifica e Tecnologica, Italy. |
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Keywords: | Nonlinear programming unconstrained optimization nondifferentiable optimization minimax problems |
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