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Numerical solution of generalized minimax problems

Ladislav Luksan(luksan***at***cs.cas.cz)
Ctirad Matonoha(matonoha***at***cs.cas.cz)
Jan Vlcek(vlcek***at***cs.cas.cz)

Abstract: This contribution contains the description and investigation of four numerical methods for solving generalized minimax problems, which consists in the minimization of functions which are compositions of special smooth convex functions with maxima of smooth functions (the most important problem of this type is the sum of maxima of smooth functions). Section~1 is introductory. In Section~2, we study recursive quadratic programming methods. This section also contains the description of the dual method for solving corresponding quadratic programming problems. Section~3 is devoted to primal interior points methods which use solutions of nonlinear equations for obtaining minimax vectors. Section~4 contains investigation of smoothing methods, based on using exponential smoothing terms. Section~5 contains a 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.

Keywords: Numerical optimization, nonlinear approximation, nonsmooth optimization, generalized minimax problems, recursive quadratic programming methods, interior point methods, smoothing methods, algorithms, numerical experiments

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Technical Report V-1255, Institute of Computer Science AVCR, Prague, January 2018

Download: [Postscript][PDF]

Entry Submitted: 05/17/2019
Entry Accepted: 05/17/2019
Entry Last Modified: 05/17/2019

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