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

Zhongyi Jiang (), Qiying Hu () and Xiaojin Zheng ()
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Zhongyi Jiang: Fudan University
Qiying Hu: Fudan University
Xiaojin Zheng: Tongji University

Journal of Global Optimization, 2017, vol. 69, issue 2, No 10, 523 pages

Abstract: 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.

Keywords: Complexity theory; Order-value optimization problem; Low order-value optimization problem; NP-hard; KKT conditions; Smooth reformulation; 90C11; 90C20; 90C25 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10898-017-0520-2

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