Duality in nonlinear programming

In this paper are defined new firstand second-order duals of the nonlinear programming problem with inequality constraints. We introduce a notion of a WD-invex problem. We prove weak, strong, converse, strict converse duality, and other theorems under the hypothesis that the problem is WD-invex. We obtain that a problem with inequality constraints is WD-invex if and only if weak duality holds between the primal and dual problems. We introduce a notion of a second-order WDinvex problem with inequality constraints. The class of WD-invex problems is strictly included in the class of second-order ones. We derive that the first-order duality results are satisfied in the second-order case.