Smooth Transformation of the Generalized Minimax Problem

G. Di Pillo, L. Grippo and S. Lucidi
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G. Di Pillo: Università di Roma “La Sapienza,”
L. Grippo: Università di Roma “La Sapienza,”
S. Lucidi: Università di Roma “La Sapienza,”

Journal of Optimization Theory and Applications, 1997, vol. 95, issue 1, No 1, 24 pages

Abstract: Abstract We consider the generalized minimax problem, that is, the problem of minimizing a function φ(x)=F(g 1(x),...,g m(x)), where F is a smooth function and each g i 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 φ. In this way, the nonsmooth original problem can be solved by usual minimization techniques for unconstrained differentiable functions.

Keywords: Nonlinear programming; unconstrained optimization; nondifferentiable optimization; generalized minimax problems; minimax problems (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/A:1022627226891

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