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December 19, 2006 9:33 Optimization amssecond Optimization

Summary: December 19, 2006 9:33 Optimization amssecond
Vol. 00, No. 00, Month-Month 200x, 1­18
On Second-Order Optimality Conditions for Nonlinear
R. Andreani
& J. M. Mart´inez
& M. L. Schuverdt§
(Received 00 Month 200x; In final form 00 Month 200x)
Necessary Optimality Conditions for Nonlinear Programming are discussed in the present research.
A new Second-Order condition is given, which depends on a weak constant rank constraint require-
ment. We show that practical and publicly available algorithms (www.ime.usp.br/egbirgin/tango)
of Augmented Lagrangian type converge, after slight modifications, to stationary points defined by
the new condition.
Key words: Nonlinear programming, Necessary Optimality Conditions, Constraint Qualifications,
Practical Algorithms.
1 Introduction
The study of Necessary Optimality Conditions (NOC) is quite relevant for
practical Nonlinear Programming. In constrained and unconstrained optimiza-
tion one is generally interested in finding global minimizers. Since this is very


Source: Andreani, Roberto - Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas


Collections: Mathematics