New regularity conditions for Lagrange and Fenchel-Lagrange duality in infinite dimensional spaces

Radu Ioan Boţ; Sorin Mihai Grad; Gert Wanka

doi:10.7153/mia-12-15

New regularity conditions for Lagrange and Fenchel-Lagrange duality in infinite dimensional spaces

Radu Ioan Boţ
, Sorin Mihai Grad
, Gert Wanka

Fac. Math. of the TU

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We give new regularity conditions expressed via epigraphs that assure strong duality between a given primal convex optimization problem and its Lagrange and Fenchel-Lagrange dual problems, respectively, in infinite dimensional spaces. Moreover we completely characterize through equivalent statements the so-called stable strong duality between the initial problem and the mentioned duals

langue originale	Anglais
Pages (de - à)	171-189
Nombre de pages	19
journal	Mathematical Inequalities and Applications
Volume	12
Numéro de publication	1
Les DOIs	https://doi.org/10.7153/mia-12-15
état	Publié - 1 janv. 2009
Modification externe	Oui

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10.7153/mia-12-15

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title = "New regularity conditions for Lagrange and Fenchel-Lagrange duality in infinite dimensional spaces",

abstract = "We give new regularity conditions expressed via epigraphs that assure strong duality between a given primal convex optimization problem and its Lagrange and Fenchel-Lagrange dual problems, respectively, in infinite dimensional spaces. Moreover we completely characterize through equivalent statements the so-called stable strong duality between the initial problem and the mentioned duals",

keywords = "Conjugate functions, Epigraphs, Fenchel-Lagrange dual, Lagrange dual, Regularity conditions",

author = "Bo{\c t}, \{Radu Ioan\} and Grad, \{Sorin Mihai\} and Gert Wanka",

year = "2009",

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AU - Boţ, Radu Ioan

AU - Grad, Sorin Mihai

AU - Wanka, Gert

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Y1 - 2009/1/1

N2 - We give new regularity conditions expressed via epigraphs that assure strong duality between a given primal convex optimization problem and its Lagrange and Fenchel-Lagrange dual problems, respectively, in infinite dimensional spaces. Moreover we completely characterize through equivalent statements the so-called stable strong duality between the initial problem and the mentioned duals

AB - We give new regularity conditions expressed via epigraphs that assure strong duality between a given primal convex optimization problem and its Lagrange and Fenchel-Lagrange dual problems, respectively, in infinite dimensional spaces. Moreover we completely characterize through equivalent statements the so-called stable strong duality between the initial problem and the mentioned duals

KW - Conjugate functions

KW - Epigraphs

KW - Fenchel-Lagrange dual

KW - Lagrange dual

KW - Regularity conditions

UR - https://www.scopus.com/pages/publications/60349099628

U2 - 10.7153/mia-12-15

DO - 10.7153/mia-12-15

M3 - Article

AN - SCOPUS:60349099628

SN - 1331-4343

VL - 12

SP - 171

EP - 189

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 1

ER -

New regularity conditions for Lagrange and Fenchel-Lagrange duality in infinite dimensional spaces

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