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Global optimality conditions for cubic minimization problem with box or binary constraints

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Abstract

In this article, we provide optimality conditions for global solutions to cubic minimization problems with box or binary constraints. Our main tool is an extension of the global subdifferential approach, developed by Jeyakumar et al. (J Glob Optim 36:471–481, 2007; Math Program A 110:521–541, 2007). We also derive optimality conditions that characterize global solutions completely in the case where the cubic objective function contains no cross terms. Examples are given to demonstrate that the optimality conditions can effectively be used for identifying global minimizers of certain cubic minimization problems with box or binary constraints.

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Authors and Affiliations

  1. Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Yanjun Wang & Zhian Liang

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  1. Yanjun Wang
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  2. Zhian Liang
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Correspondence to Yanjun Wang.

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Wang, Y., Liang, Z. Global optimality conditions for cubic minimization problem with box or binary constraints. J Glob Optim 47, 583–595 (2010). https://doi.org/10.1007/s10898-009-9480-5

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  • DOI: https://doi.org/10.1007/s10898-009-9480-5

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