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Strong Duality and Dual Pricing Properties in Semi-infinite Linear Programming--A Non-Fourier-Motzkin Elimination Approach

Qinghong Zhang(qzhang***at***nmu.edu)

Abstract: The Fourier-Motzkin elimination method has been recently extended to linear inequality systems that have infinitely many inequalities. It has been used in the study of linear semi-infinite programming by Basu, Martin, and Ryan. Following the idea of the conjecture for semi-infinite programming in a paper by Kortanek and Zhang recently published in Optimization, which states ``all the duality results proved by applying FM (the Fourier-Motzkin elimination method) first can also be obtained by working with the problem directly", in this paper without using the Fourier-Motzkin elimination, we reproduce all the results presented in a recent paper by Basu, Martin, and Ryan on the strong duality and dual pricing properties in semi-infinite programming in which the main mechanism is the Fourier-Motzkin elimination. We also present some new results regarding the strong duality and dual pricing properties, which are the main topics in Basu-Martin-Ryan's paper.

Keywords: Semi-infinite programming; Strong duality property; Dual pricing property

Category 1: Infinite Dimensional Optimization (Semi-infinite Programming )


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Entry Submitted: 02/13/2016
Entry Accepted: 02/13/2016
Entry Last Modified: 02/13/2016

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