Summary: J Optim Theory Appl
Constant-Rank Condition and Second-Order
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
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.