Smooth Transformation of the Generalized 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,, Roma, Italy;(2) Dipartimento di Informatica e Sistemistica, Università di Roma La Sapienza,, Roma, Italy |
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Abstract: | We consider the generalized minimax problem, that is, the problem of minimizing a function (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. |
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Keywords: | Nonlinear programming unconstrained optimization nondifferentiable optimization generalized minimax problems minimax problems |
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