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Duality Theory for Optimization Problems with Interval-Valued Objective Functions

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Abstract

A solution concept in optimization problems with interval-valued objective functions, which is essentially similar to the concept of nondominated solution in vector optimization problems, is introduced by imposing a partial ordering on the set of all closed intervals. The interval-valued Lagrangian function and interval-valued Lagrangian dual function are also proposed to formulate the dual problem of the interval-valued optimization problem. Under this setting, weak and strong duality theorems can be obtained.

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Authors and Affiliations

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

    H. C. Wu

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  1. H. C. Wu
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Correspondence to H. C. Wu.

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Communicated by F. Giannessi.

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Wu, H.C. Duality Theory for Optimization Problems with Interval-Valued Objective Functions. J Optim Theory Appl 144, 615–628 (2010). https://doi.org/10.1007/s10957-009-9613-5

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  • DOI: https://doi.org/10.1007/s10957-009-9613-5

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