Saddle points criteria in nondifferentiable multiobjective programming with V-invex functions via an η-approximation method

  • Authors:

  • Tadeusz Antczak

  • Affiliations:

  • -

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

The @h-approximation method is used to a characterization of solvability of nonconvex nondifferentiable multiobjective programming problems. A family of @h-approximated vector optimization problems is constructed in this approach for the original nondifferentiable multiobjective programming problem. The definitions of a vector-valued @h-Lagrange function and of an @h-saddle point for this family of @h-approximated vector optimization problems are introduced. Thus, the equivalence between a (weak) Pareto optimum of the original multiobjective programming problems and an @h-saddle point of the @h-Lagrange function in its associated @h-approximated vector optimization problems is established under V-invexity.