Strong Duality in Robust Convex Programming: Complete Characterizations

Jeyakumar, V.; Li, Guoyin

doi:10.1137/100791841

Cited by 124 publications

(65 citation statements)

References 16 publications

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“…Chong et.al derived Sufficient and necessary conditions for the stable Fenchel duality and for the total Fenchel duality , also proved some sufficient and necessary conditions for the strong Fenchel duality and the strong converse Fenchel duality using the properties of the epigraph of the conjugated functions [14]. Jeyakumar et al developed a robust theorem of the alternative for parameterized convex inequality systems using conjugate analysis and derives a new robust characteristic cone constraint qualification necessary and sufficient for strong duality between the robust equivalent and its Lagrangian dual [15]. Wang et.al establishes some total and strong Fenchel dualities for convex optimization problems accompanying data uncertainty within the framework of robust optimization in locally convex Hausdorff vector spaces [16].…”

Section: Introductionmentioning

confidence: 99%

Optimization of convex functions with fenchel biconjugation and duality

Bhardwaj¹

2018

IJATEE

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Section: Introductionmentioning

confidence: 99%

Optimization of convex functions with fenchel biconjugation and duality

Bhardwaj¹

2018

IJATEE

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“…Robust convex optimization [3,4,5,11,16,17] deals with solutions of robust counterparts of uncertain convex programs where the data uncertainty is treated as deterministic, as opposed to stochastic that is used in stochastic programming. It has emerged as a powerful numerically tractable approach to treat uncertainty in convex programming.…”

Section: Introductionmentioning

confidence: 99%

Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints

Goberna¹,

Jeyakumar²,

Li³

et al. 2016

Operations Research Letters

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The radius of robust feasibility of a convex program with uncertain constraints gives a value for the maximal 'size' of an uncertainty set under which robust feasibility can be guaranteed. This paper provides an upper bound for the radius for convex programs with uncertain convex polynomial constraints and exact formulas for convex programs with SOS-convex polynomial constraints (or convex quadratic constraints) under affine data uncertainty. These exact formulas allow the radius to be computed by commonly available software.

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“…The present work was motivated by the recent development of robust duality theory [1,21] for convex programming problems in the face of data uncertainty. To set the context of this work, consider a standard form of linear semi-in…nite programming (SIP) problem in the absence of data uncertainty:…”

Section: Introductionmentioning

confidence: 99%

Robust linear semi-infinite programming duality under uncertainty

Goberna

Jeyakumar

et al. 2013

Math. Program.

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In this paper, we propose a duality theory for semi-in…nite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-in…nite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then show that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and su¢ cient for robust duality in the sense that robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with a¢ nely parameterized data uncertainty, we establish that robust duality is easily satis…ed under a Slater type constraint quali…cation. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-in…nite linear inequalities.

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Strong Duality in Robust Convex Programming: Complete Characterizations

Cited by 124 publications

References 16 publications

Optimization of convex functions with fenchel biconjugation and duality

Optimization of convex functions with fenchel biconjugation and duality

Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints

Robust linear semi-infinite programming duality under uncertainty

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