Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming
نویسندگان
چکیده
منابع مشابه
Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming
For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverse-convex inequalities which are consequence of the constrained syst...
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Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...
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This paper deals with optimality conditions to solve nonlinear programming problems. The classical Karush-Kuhn-Tucker (KKT) optimality conditions are demonstrated through a cone approach, using the well known Farkas’ Lemma. These conditions are valid at a minimizer of a nonlinear programming problem if a constraint qualification is satisfied. First we prove the KKT theorem supposing the equalit...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2010
ISSN: 1052-6234,1095-7189
DOI: 10.1137/080739124