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Optimality condition and complexity of order-value optimization problems and low order-value optimization problems

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Abstract

Order-value optimization problems and low order-value optimization problems are new subclasses of optimization problems which arise from decision-making problems under uncertainty and robust estimation problems. In this paper, We present KKT necessary and sufficient conditions for low order-value optimization problems under convexity hypothesis in this paper. A smooth reformulation of low order-value optimization problems are presented whose local solutions satisfy the KKT necessary conditions. we prove that order-value optimization problems is NP-hard in the strong sense even when constraints are polytope. Order-value optimization problems and low order-value optimization problems are NP-hard even when their presentation functions are linear and constraints are polytope. Some special cases that could be solved in polynomial time are proposed.

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Acknowledgements

The authors are very grateful for the reviewers’ valuable comments to improve the quality of the paper.

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Correspondence to Xiaojin Zheng.

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This research is supported in part by National Natural Science Foundation of China under Grants 11371103; 71671046 and 11671300.

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Jiang, Z., Hu, Q. & Zheng, X. Optimality condition and complexity of order-value optimization problems and low order-value optimization problems. J Glob Optim 69, 511–523 (2017). https://doi.org/10.1007/s10898-017-0520-2

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  • DOI: https://doi.org/10.1007/s10898-017-0520-2

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