Non-differentiable multiobjective programming under generalised functions

In this paper, we consider a nonlinear multiobjective programming problem where functions involved are non-differentiable. The use of directional derivative in association with a hypothesis of an invex kind on the set has been of much interest in the recent past. Recently under preinvexity assumptions on fi′(xo;ηi(x,xo)) and g′j (xo;θj(x,xo)), necessary and sufficient optimality conditions for a non-smooth multiobjective optimisation problem under generalised class of dI-V-type I functions have been derived. Working in this direction, we introduce a new class of (φ, dI)-V-type I functions and illustrate through various non-trivial examples that this class is non-empty and extends some known classes introduced in the literature. Also, we obtain sufficient optimality conditions to enable a feasible solution of the primal problem to be its weak efficient/efficient solution. Then through an example, we illustrate the relevance of the sufficient optimality theorem obtained to get the efficient solu...