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Global optimality conditions for cubic minimization problems with cubic constraints

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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.

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Acknowledgments

The authors are grateful to the responsible editor and the anonymous referees for their valuable comments and suggestions, which have improved the earlier version of this paper. Thanks to the support by the Ph.D. Start-up Fund of Natural Science Foundation of Guangdong Province, China (No. S2013040012506) and China Postdoctoral Science Foundation Funded Project (2014M562152).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, 510006, Guangdong, China

    Xue-Gang Zhou, Xiao-Peng Yang & Bing-Yuan Cao

  2. Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, 510521, Guangdong, China

    Xue-Gang Zhou

  3. Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong, China

    Xiao-Peng Yang

  4. Guangzhou Vocational College of Science and Technology, Guangzhou, 510550, Guangdong, China

    Bing-Yuan Cao

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  1. Xue-Gang Zhou
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  2. Xiao-Peng Yang
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  3. Bing-Yuan Cao
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Correspondence to Bing-Yuan Cao.

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Zhou, XG., Yang, XP. & Cao, BY. Global optimality conditions for cubic minimization problems with cubic constraints. Math Meth Oper Res 82, 243–264 (2015). https://doi.org/10.1007/s00186-015-0511-3

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  • DOI: https://doi.org/10.1007/s00186-015-0511-3

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