# New Farkas-type constraint qualifications in convex infinite programming

Nguyen Dinh; Miguel A. Goberna; Marco A. López; Ta Quang Son

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 13, Issue: 3, page 580-597
- ISSN: 1292-8119

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topDinh, Nguyen, et al. "New Farkas-type constraint qualifications in convex infinite programming." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 580-597. <http://eudml.org/doc/249989>.

@article{Dinh2007,

abstract = {
This paper provides KKT and saddle point optimality conditions, duality
theorems and stability theorems for consistent convex optimization problems
posed in locally convex topological vector spaces. The feasible sets of
these optimization problems are formed by those elements of a given closed
convex set which satisfy a (possibly infinite) convex system. Moreover, all
the involved functions are assumed to be convex, lower semicontinuous and
proper (but not necessarily real-valued). The key result in the paper is the
characterization of those reverse-convex inequalities which are consequence
of the constraints system. As a byproduct of this new versions of Farkas'
lemma we also characterize the containment of convex sets in reverse-convex
sets. The main results in the paper are obtained under a suitable
Farkas-type constraint qualifications and/or a certain closedness assumption.
},

author = {Dinh, Nguyen, Goberna, Miguel A., López, Marco A., Son, Ta Quang},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Convex infinite programming; KKT and saddle point optimality conditions; duality theory; Farkas-type constraint qualification; convex infinite programming},

language = {eng},

month = {6},

number = {3},

pages = {580-597},

publisher = {EDP Sciences},

title = {New Farkas-type constraint qualifications in convex infinite programming},

url = {http://eudml.org/doc/249989},

volume = {13},

year = {2007},

}

TY - JOUR

AU - Dinh, Nguyen

AU - Goberna, Miguel A.

AU - López, Marco A.

AU - Son, Ta Quang

TI - New Farkas-type constraint qualifications in convex infinite programming

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2007/6//

PB - EDP Sciences

VL - 13

IS - 3

SP - 580

EP - 597

AB -
This paper provides KKT and saddle point optimality conditions, duality
theorems and stability theorems for consistent convex optimization problems
posed in locally convex topological vector spaces. The feasible sets of
these optimization problems are formed by those elements of a given closed
convex set which satisfy a (possibly infinite) convex system. Moreover, all
the involved functions are assumed to be convex, lower semicontinuous and
proper (but not necessarily real-valued). The key result in the paper is the
characterization of those reverse-convex inequalities which are consequence
of the constraints system. As a byproduct of this new versions of Farkas'
lemma we also characterize the containment of convex sets in reverse-convex
sets. The main results in the paper are obtained under a suitable
Farkas-type constraint qualifications and/or a certain closedness assumption.

LA - eng

KW - Convex infinite programming; KKT and saddle point optimality conditions; duality theory; Farkas-type constraint qualification; convex infinite programming

UR - http://eudml.org/doc/249989

ER -

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