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

Abstract. 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.

• Type: Conference
• Year: 2003
• Where: ICCSA
• Authors: Olga Brezhneva, Alexey Tret'yakov
• Keywords: Active Constraint Gradients, Applied Computing, Degenerate Case, ICCSA 2003, Necessary Optimality Conditions