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Duality Theory in Interval-Valued Linear Programming Problems

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Abstract

The weak and strong duality theorems in interval-valued linear programming problems are derived in this paper. The primal and dual interval-valued linear programming problems are formulated by proposing the concept of a scalar (inner) product of closed intervals. We introduce a solution concept that is essentially similar to the notion of nondominated solution in multiobjective programming problems by imposing a partial ordering on the set of all closed intervals. Under these settings, the weak and strong duality theorems for interval-valued linear programming problems are derived naturally.

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Authors and Affiliations

  1. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 802, Taiwan

    Hsien-Chung Wu

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  1. Hsien-Chung Wu
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Correspondence to Hsien-Chung Wu.

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Communicated by J. Jahn.

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Wu, HC. Duality Theory in Interval-Valued Linear Programming Problems. J Optim Theory Appl 150, 298–316 (2011). https://doi.org/10.1007/s10957-011-9842-2

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  • DOI: https://doi.org/10.1007/s10957-011-9842-2

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