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Checking weak optimality of the solution to interval linear program in the general form

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Abstract

One of the basic and difficult tasks in interval linear programming (IvLP) problems is to check whether a given point is weak optimal. In this paper, we investigate IvLP problem in the general form, in which the constraints contain mixed interval linear equations and inequalities with both non-negative and free variables. Necessary and sufficient conditions for checking weak optimality of a given vector are established, based on the KKT conditions of linear programming and the newly established weak solvability characterizations of mixed interval linear systems by Hladík. The result solves one of the open problems proposed by Hladík (Linear Programming New Frontiers. Nova Science Publishers, Inc 2012).

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Acknowledgments

We are grateful to an anonymous referee for his/her valuable suggestions which led to improvements in the current version. The remarks at the ends of Sects. 3 and 4 are base on his/her suggestions. We are also grateful to the editor for his/her valuable comments, which have helped us to improve the quality of the article. The authors were partially supported by the NSF of Zhejiang Province (Grant No. LY14A010028) and NNSF of China (Grant No. 11171316).

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Authors and Affiliations

  1. Institute of Operational Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, 310018, China

    Wei Li & Pengzhen Liu

  2. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, China

    Haohao Li

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  1. Wei Li
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  2. Pengzhen Liu
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  3. Haohao Li
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Correspondence to Haohao Li.

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Li, W., Liu, P. & Li, H. Checking weak optimality of the solution to interval linear program in the general form. Optim Lett 10, 77–88 (2016). https://doi.org/10.1007/s11590-015-0856-9

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  • DOI: https://doi.org/10.1007/s11590-015-0856-9

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