Farkas-type results for general composed convex optimization problems with inequality constraints

Xian Jun Long; Nan Jing Huang; Donal O'Regan

doi:10.7153/mia-13-10

Farkas-type results for general composed convex optimization problems with inequality constraints

Xian Jun Long, Nan Jing Huang, Donal O'Regan

Mathematics

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6 Citations (Scopus)

Abstract

In this paper, we consider a general composed convex optimization problem with inequality systems involving a finite number of convex constraints. We establish the strong duality between the primal problem and the Fenchel-Lagrange dual problem by a conjugate duality approach. Moreover, we obtain some new Farkas-type results for this problem by using weak and strong duality theorems. Our results contain some recent results as special cases.

Original language	English
Pages (from-to)	135-143
Number of pages	9
Journal	Mathematical Inequalities and Applications
Volume	13
Issue number	1
DOIs	https://doi.org/10.7153/mia-13-10
Publication status	Published - Jan 2010

Keywords

Conjugate dual
Farkas-type results
Fenchel-lagrange duality
Finitely many convex constraints
General composed convex optimization problems

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10.7153/mia-13-10

Cite this

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abstract = "In this paper, we consider a general composed convex optimization problem with inequality systems involving a finite number of convex constraints. We establish the strong duality between the primal problem and the Fenchel-Lagrange dual problem by a conjugate duality approach. Moreover, we obtain some new Farkas-type results for this problem by using weak and strong duality theorems. Our results contain some recent results as special cases.",

keywords = "Conjugate dual, Farkas-type results, Fenchel-lagrange duality, Finitely many convex constraints, General composed convex optimization problems",

author = "Long, \{Xian Jun\} and Huang, \{Nan Jing\} and Donal O'Regan",

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AU - Huang, Nan Jing

AU - O'Regan, Donal

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N2 - In this paper, we consider a general composed convex optimization problem with inequality systems involving a finite number of convex constraints. We establish the strong duality between the primal problem and the Fenchel-Lagrange dual problem by a conjugate duality approach. Moreover, we obtain some new Farkas-type results for this problem by using weak and strong duality theorems. Our results contain some recent results as special cases.

AB - In this paper, we consider a general composed convex optimization problem with inequality systems involving a finite number of convex constraints. We establish the strong duality between the primal problem and the Fenchel-Lagrange dual problem by a conjugate duality approach. Moreover, we obtain some new Farkas-type results for this problem by using weak and strong duality theorems. Our results contain some recent results as special cases.

KW - Conjugate dual

KW - Farkas-type results

KW - Fenchel-lagrange duality

KW - Finitely many convex constraints

KW - General composed convex optimization problems

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EP - 143

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 1

ER -

Farkas-type results for general composed convex optimization problems with inequality constraints

Abstract

Keywords

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