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

Research output: Contribution to journal › Article › peer-review

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

Original language	English
Pages (from-to)	171-189
Number of pages	19
Journal	Mathematical Inequalities and Applications
Volume	12
Issue number	1
DOIs	https://doi.org/10.7153/mia-12-15
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Conjugate functions
Epigraphs
Fenchel-Lagrange dual
Lagrange dual
Regularity conditions

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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",

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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

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

Abstract

Keywords

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