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Paper   IPM / M / 14050
School of Mathematics
  Title:   Optimality conditions for isolated local minimum of nonsmooth multiobjective problems
  Author(s):  S. Nobakhtian (Joint with A. Ansari)
  Status:   Published
  Journal: Numerical Functional Analysis and Optimization
  Vol.:  36
  Year:  2015
  Pages:   1087-1106
  Supported by:  IPM
This article is devoted to the study of Fritz John and strong Kuhn-Tucker necessary conditions for properly efficient solutions, efficient solutions and isolated efficient solutions of a nonsmooth multiobjective optimization problem involving inequality and equality constraints and a set constraints in terms of the lower Hadamard directional derivative. Sufficient conditions for the existence of such solutions are also provided where the involved functions have pseudoconvex sublevel sets. Our results are based on the concept of pseudoconvex sublevel sets. The functions with pseudoconvex sublevel sets are a class of generalized convex functions that include quasiconvex functions.

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