Duality in nonlinear programming

In this paper are defined new first‐ and 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 WD‐invex 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.