Hartley Proper Efficiency in Multiobjective Optimization Problems with Locally Lipschitz Set-valued Objectives and Constraints

  • Authors:

  • P. H. Sach

  • Affiliations:

  • Hanoi Institute of Mathematics, Hanoi, Vietnam 10307

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2006

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Abstract

In this paper we give necessary conditions for Hartley proper efficiency in a vector optimization problem whose objectives and constraints are described by nonconvex locally Lipchitz set-valued maps. The obtained necessary conditions are written in terms of a Lagrange multiplier rule. Our approach is based on a reduction theorem which leads the problem of studying proper efficiency to a scalar optimization problem whose objective is given by a function of max-type. Sufficient conditions for Hartley proper efficiency are also considered.