Post-Optimal Analysis of Linear Semi-Infinite Programs

Goberna, Miguel Á.

doi:10.1007/978-0-387-89496-6_2

Cited by 10 publications

(1 citation statement)

References 78 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, most duality theory has been developed for the finite support dual [3,5,6,10,12,14]. Moreover, the only other dual given significant attention in the literature is the "continuous dual" (see for instance [4,7]) and this dual shares many of the same duality properties as the finite support dual. Indeed, as stated by Goberna in [4]: "all known duality theorems guaranteeing the existence of a zero duality gap have the same hypotheses for both dual problems [the finite support dual and the continuous dual]".…”

Section: Introductionmentioning

confidence: 99%

On the sufficiency of finite support duals in semi-infinite linear programming

Basu

Martin

Ryan

2014

Operations Research Letters

View full text Add to dashboard Cite

We consider semi-infinite linear programs with countably many constraints indexed by the natural numbers. When the constraint space is the vector space of all real valued sequences, we show that the finite support (Haar) dual is equivalent to the algebraic Lagrangian dual of the linear program. This settles a question left open by Anderson and Nash [2]. This result implies that if there is a duality gap between the primal linear program and its finite support dual, then this duality gap cannot be closed by considering the larger space of dual variables that define the algebraic Lagrangian dual. However, if the constraint space corresponds to certain subspaces of all realvalued sequences, there may be a strictly positive duality gap with the finite support dual, but a zero duality gap with the algebraic Lagrangian dual.

show abstract