Numerical Solution of Generalized Minimax Problems

Ladislav Lukšan (), Ctirad Matonoha () and Jan Vlček ()
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Ladislav Lukšan: The Czech Academy of Sciences, Institute of Computer Science
Ctirad Matonoha: The Czech Academy of Sciences, Institute of Computer Science
Jan Vlček: The Czech Academy of Sciences, Institute of Computer Science

Chapter Chapter 11 in Numerical Nonsmooth Optimization, 2020, pp 363-414 from Springer

Abstract: Abstract This contribution contains the description and investigation of three numerical methods for solving generalized minimax problems. These problems consists in the minimization of nonsmooth functions which are compositions of special smooth convex functions with maxima of smooth functions. The most important functions of this type are the sums of maxima of smooth functions. Section 11.2 is devoted to primal interior point methods which use solutions of nonlinear equations for obtaining minimax vectors. Section 11.3 contains investigation of smoothing methods, based on using exponential smoothing terms. Section 11.4 contains short description of primal-dual interior point methods based on transformation of generalized minimax problems to general nonlinear programming problems. Finally the last section contains results of numerical experiments.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-34910-3_11

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DOI: 10.1007/978-3-030-34910-3_11

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