On generalised convex mathematical programming

Abstract

Abstract The sufficient optimality conditions and duality results have recently been given for the following generalised convex programming problem: where the funtion f and g satisfy for some η: X 0 × X 0 → ℝ n It is shown here that a relaxation defining the above generalised convexity leads to a new class of multi-objective problems which preserves the sufficient optimality and duality results in the scalar case, and avoids the major difficulty of verifying that the inequality holds for the same function η(. , .). Further, this relaxation allows one to treat certain nonlinear multi-objective fractional programming problems and some other classes of nonlinear (composite) problems as special cases.