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

• Published in: Mathematics of operations research Vol. 31; no. 1; pp. 1 - 12
• Main Authors: Arutyunov, Aram, Pereira, Fernando Lobo
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01-02-2006; Institute for Operations Research and the Management Sciences
• Subjects: A priori knowledge; Analysis; Case studies; curvature effect; Finite spaces; Lagrange multipliers; Management science; Mathematical functions; Mathematical optimization; Mathematical theorems; Mathematical vectors; Necessary conditions for optimality; nondegeneracy; Nonlinear programming; Optimization algorithms; second-order necessary conditions of optimality; Studies; Topological spaces; Topological vector spaces
• ISSN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.1050.0172

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.