The p-th Order Necessary Optimality Conditions for Inequality-Constrained Optimization Problems

摘要

In this paper, we consider a nonlinear optimization problem with inequality constraints. The paper addresses the degenerate case when the active constraint gradients are linearly dependent at the solution, and the Mangasarian-Fromovitz constraint qualification fails to hold. For this case, we present new generalized p-order necessary optimality conditions. The conditions subsume the classical conditions and give new and nontrivial conditions for the degenerate case. The presented results can be considered as a part of the p-regularity theory.