Global optimality conditions for cubic minimization problems with cubic constraints

Xue-Gang Zhou, Xiao-Peng Yang and Bing-Yuan Cao ()

Mathematical Methods of Operations Research, 2015, vol. 82, issue 3, 243-264

Abstract: In this paper, we present global optimality conditions for cubic minimization involving cubic constraints and box or bivalent constraints, where the cubic objective function and cubic constraints contain no cross terms. By utilizing quadratic underestimators, we first derive sufficient global optimality conditions for a global minimizer of cubic minimization problems with cubic inequality and box constraints. Then we establish them for cubic minimization with cubic inequality and bivalent constraints. Finally, we establish sufficient and necessary global optimality condition for cubic minimization with cubic equality and binary constraints. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Cubic minimization; Global optimality conditions; Quadratic underestimators; 90C26; 90C30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00186-015-0511-3

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