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J Optim Theory Appl DOI 10.1007/s10957-010-9671-8

Summary: J Optim Theory Appl
DOI 10.1007/s10957-010-9671-8
Constant-Rank Condition and Second-Order
Constraint Qualification
R. Andreani · C.E. Echagüe · M.L. Schuverdt
© Springer Science+Business Media, LLC 2010
Abstract The constant-rank condition for feasible points of nonlinear programming
problems was defined by Janin (Math. Program. Study 21:127­138, 1984). In that
paper, the author proved that the constant-rank condition is a first-order constraint
qualification. In this work, we prove that the constant-rank condition is also a second-
order constraint qualification. We define other second-order constraint qualifications.
Keywords Nonlinear programming · Constraint qualifications
1 Introduction
We are concerned with the general nonlinear programming problems with equality
and inequality constraints in the form
minf (x), s.t. h(x) = 0, g(x) 0, (1)
Communicated by F. Giannessi.
This research was supported by PRONEX-Optimization 76.79.1008-00, FAPESP (Grant
01-04597-4) and CNPq.
R. Andreani


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


Collections: Mathematics