Optimality conditions for semi-infinite programming problems involving generalized convexity

Original Paper


We apply some advanced tools of quasiconvex analysis to establish Karush–Kuhn–Tucker type necessary and sufficient optimality conditions for non-differentiable semi-infinite programming problems. In addition, we propose a linear characterization of optimality for the mentioned problems. Examples are also designed to analyze and illustrate the results obtained.


Semi-infinite programming Plastria function Gutiérrez functions Optimality conditions Linear characterization 



The authors are grateful to professor Miguel Ángel Goberna for his many helpful suggestions which have improved the presentation of the paper. Also, we would like to thank the three anonymous referees for carefully reading our work and for their helpful comments.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsPayame Noor University (PNU)TehranIran
  2. 2.Department of EconomicsUniversity of MessinaMessinaItaly
  3. 3.Department of Mathematics, Yazd BranchIslamic Azad UniversityYazdIran

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