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Second-Order Necessary Optimality Conditions for Problems Without A Priori Normality Assumptions

Differential Equations and Functional Analysis Dept., Peoples Friendship University of Russia, 6 Mikluka-Maklai Street, Moscow 117198
Instituto de Sistemas e Robótica, Faculdade de Engenharia da Universidade do Porto, R. Dr. Roberto Frias, 4200-465 Porto, Portugal
arutun{at}orc.ru
flp{at}fe.up.pt

In this article, we derive second-order necessary conditions of optimality for an abstract optimization problem with equality and inequality constraints and constraints in the form of an inclusion into a given closed set. An important feature is that our optimality conditions dispense with any a priori normality assumptions, such as Robinson’s constraint qualification, and remain informative even for abnormal points. Moreover, our optimality conditions take into account the second-order effect of the curvature of the set in the inclusion constraints.

Key Words: second-order necessary conditions of optimality; nondegeneracy; curvature effect
History: Received: October 16, 2004; revision received: March 12, 2005;