Optimality and Duality in Nondifferentiable Multiobjective Optimization Involving d-Type I and Related Functions

In this paper new classes of functions, namely d-type-I, d-quasitype-I, and d-pseudo type-I, are defined for a multiobjective nondifferentiable programming problem. Kuhn]Tucker-type necessary and sufficient optimality conditions are obtained for a feasible point to be a weak minimum for this problem. Two duals are formulated and various duality results are given by using the above defined classes of functions, considering the concept of a weak minimum.