We consider the generalized minimax problem, that is, the problem of minimizing a function (j>(x) = F(g1 (x),..., gm(x)), where F is a smooth function and each gi is the maximum of a finite number of smooth functions. We prove that, under suitable assumptions, it is possible to construct a continuously differentiable exact barrier function, whose minimizers yield the minimizers of the function <j>. In this way, the nonsmooth original problem can be solved by usual minimization techniques for unconstrained differentiable functions.

A smooth transformation of the generalized minimax problem / DI PILLO, Gianni; Grippo, Luigi; Lucidi, Stefano. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - STAMPA. - 95:(1997), pp. 1-24. [10.1023/A:1022627226891]

A smooth transformation of the generalized minimax problem

DI PILLO, Gianni;GRIPPO, Luigi;LUCIDI, Stefano
1997

Abstract

We consider the generalized minimax problem, that is, the problem of minimizing a function (j>(x) = F(g1 (x),..., gm(x)), where F is a smooth function and each gi is the maximum of a finite number of smooth functions. We prove that, under suitable assumptions, it is possible to construct a continuously differentiable exact barrier function, whose minimizers yield the minimizers of the function . In this way, the nonsmooth original problem can be solved by usual minimization techniques for unconstrained differentiable functions.
1997
Nonlinear programming; unconstrained optimization; nondifferentiable optimization; generalized minimax problems; minimax problems.
01 Pubblicazione su rivista::01a Articolo in rivista
A smooth transformation of the generalized minimax problem / DI PILLO, Gianni; Grippo, Luigi; Lucidi, Stefano. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - STAMPA. - 95:(1997), pp. 1-24. [10.1023/A:1022627226891]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/247511
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