Generalizations of Slater's constraint qualification for infinite convex programs
Mathematical Programming: Series A and B
Convex Optimization
Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems
Mathematical Programming: Series A and B
Stochastic programming approach to optimization under uncertainty
Mathematical Programming: Series A and B
Selected topics in robust convex optimization
Mathematical Programming: Series A and B
Complete characterizations of stable Farkas’ lemma and cone-convex programming duality
Mathematical Programming: Series A and B
SIAM Journal on Optimization
On Extension of Fenchel Duality and its Application
SIAM Journal on Optimization
Stable and Total Fenchel Duality for Convex Optimization Problems in Locally Convex Spaces
SIAM Journal on Optimization
Constructing Uncertainty Sets for Robust Linear Optimization
Operations Research
SIAM Journal on Optimization
Operations Research Letters
Duality in robust optimization: Primal worst equals dual best
Operations Research Letters
Robust linear optimization under general norms
Operations Research Letters
A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty
Operations Research Letters
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Duality theory has played a key role in convex programming in the absence of data uncertainty. In this paper, we present a duality theory for convex programming problems in the face of data uncertainty via robust optimization. We characterize strong duality between the robust counterpart of an uncertain convex program and the optimistic counterpart of its uncertain Lagrangian dual. We provide a new robust characteristic cone constraint qualification which is necessary and sufficient for strong duality in the sense that the constraint qualification holds if and only if strong duality holds for every convex objective function of the program. We further show that this strong duality always holds for uncertain polyhedral convex programming problems by verifying our constraint qualification, where the uncertainty set is a polytope. We derive these results by way of first establishing a robust theorem of the alternative for parameterized convex inequality systems using conjugate analysis. We also give a convex characteristic cone constraint qualification that is necessary and sufficient for strong duality between the deterministic dual pair: the robust counterpart and its Lagrangian dual. Through simple numerical examples we also provide an insightful account of the development of our duality theory.