On global unconstrained minimization of the difference of polyhedral functions

Authors:
Lyudmila N. Polyakova
Affiliations:
Department of Applied Mathematics and Control Processes, Saint-Petersburg University, Saint-Petersburg, Russia 198504
Venue:
Journal of Global Optimization
Year:
2011

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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.