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Paper   IPM / M / 14990
School of Mathematics
  Title:   Multiobjective problems: Enhanced necessary conditions and new constraint qualifications via convexificators
  Author(s):  Soghra Nobakhtian (Joint with M. Alavi Hejazi and N. Movahedian)
  Status:   Published
  Journal: Numerical Functional Analysis and Optimization
  Vol.:  39
  Year:  2018
  Pages:   11-37
  Supported by:  IPM
  Abstract:
In this paper, we study necessary optimality conditions for local Pareto and weak Pareto solutions of multiobjective problems involving inequality and equality constraints in terms of convexificators. We develop the enhanced Karush-Kuhn-Tucker conditions and introduce the associated pseudonormality and quasinormality conditions. We also introduce several other new constraint qualifications which entirely depend on the feasible set. Then a connecting link between these constraint qualifications is presented. Moreover, we provide a number of examples that clarify the interrelations between the different results that we have established.

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