Optimality conditions for an exhausterable function on an exhausterable set

  • Majid E. AbbasovEmail author


Exhausters are families of convex compact sets that allow one to represent directional derivative of the studied function at a point in the form of InfMax or SupMin of linear functions. Functions for which such a representation is valid we call exhausterable. This class of functions is quite wide and contains many nonsmooth ones. The set of exhausterable function is also called exhausterable. In the present paper we describe optimality conditions for an exhausterable function on an exhausterable set. These conditions can be used for solving many nondifferentiable optimization problems. An example that illustrate obtained results is provided.


Exhausters Nonsmooth analysis Nondifferentiable optimization Constrained optimization Optimality conditions 

Mathematics Subject Classification

49J52 90C46 90C47 



The reported study was supported by Russian Science Foundation, Research Project No. 18-71-00006.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St. Petersburg State University, SPbSUSt. PetersburgRussia

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