Numerical Nonsmooth Optimization

0522789 - ÚI 2021 RIV CH eng M - Monography Chapter
Lukšan, Ladislav - Matonoha, Ctirad - Vlček, Jan
Numerical Solution of Generalized Minimax Problems.
Numerical Nonsmooth Optimization. Cham: Springer, 2020 - (Bagirov, A.; Gaudioso, M.; Karmitsa, N.; Mäkelä, M.; Taheri, S.), s. 363-414. ISBN 978-3-030-34909-7
Institutional support: RVO:67985807
Keywords : Numerical optimization * nonlinear approximation * nonsmooth optimization * generalized minimax problems * interior point methods * smoothing methods * algorithms * numerical experiments
OECD category: Pure mathematics
https://doi.org/10.1007/978-3-030-34910-3

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.
Permanent Link: http://hdl.handle.net/11104/0307221