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On global unconstrained minimization of the difference of polyhedral functions

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Abstract

The problem of finding a global minimizer of the difference of polyhedral functions is considered. By means of conjugate functions, necessary and sufficient conditions for the unboundedness and the boundedness of such functions in R n are derived. Using hypodifferentials of polyhedral functions, necessary and sufficient conditions for a global unconstrained minimum on R n are proved.

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  1. Department of Applied Mathematics and Control Processes, Saint-Petersburg University, Universitetskii prospekt 35, Petergof, Saint-Petersburg, 198504, Russia

    Lyudmila N. Polyakova

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  1. Lyudmila N. Polyakova
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Polyakova, L.N. On global unconstrained minimization of the difference of polyhedral functions. J Glob Optim 50, 179–195 (2011). https://doi.org/10.1007/s10898-010-9589-6

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  • DOI: https://doi.org/10.1007/s10898-010-9589-6

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