On the Relations Between Different Dual Problems in Convex Mathematical Programming

Abstract

Using the Fenchel-Rockafellar approach for the convex mathematical programming problem with inequality constraints different dual optimization problems by means of distinct perturbations of the primal problem are derived and studied. The classical Lagrange dual problem is one of those dual problems obtained by the perturbation of the right hand side of the inequality constraints. For the various dual problems equality/inequality relations between the optimum values are verified under appropriate assumptions. Moreover, the duality relations to the primal problem are considered, in particular strong duality. Using the dual problems some optimality conditions are established.