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

Abstract

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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.

How to cite

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Dinh, 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 -

References

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