ε-optimality for multiobjective programming on a Banach space

Abstract

We establish a Lagrange multiplier rule, in terms of Clarke generalized gradient, that characterizes ε-efficiency of a nondifferentiable multiobjective programming problem on a real Banach space. This rule is then utilized to establish relationship between ε-efficient solution of multiobjective program and generalized saddle point of an appropriate vector-valued Lagrangian under invexity hypothesis.