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Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem

机译：特殊三次最小化问题的全局最优性条件

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摘要

We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006). The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006) and Y. Wang et al. (2010). Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
机译：通过扩展V.Jeyakumar等人提出的全局次微分方法，我们为带有框约束或二元约束的特殊三次最小化问题提供了一些充分的全局最优性条件。 （2006）。当前条件概括了V. Jeyakumar等人的工作中得出的结果。考虑了具有箱约束或二元约束的二次最小化问题。另外，构造了一个特殊的对角矩阵，该矩阵用于提供一种简便的方法来证明所提出的充分条件。然后，重新制定充分条件。值得注意的是，这种重新定义也适用于V. Jeyakumar等人的工作中考虑的具有盒子或二进制约束的二次最小化问题。 （2006）和Y. Wang等。 （2010）。最后，一些例子表明我们的最优性条件可以有效地用于确定某些非凸三次最小化问题的全局最小化子。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第8期|871741.1-871741.16|共16页
  • 作者

    Xiaomei Zhang; Yanjun Wang; Weimin Ma;

  • 作者单位

    Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China;

    Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China;

    School of Economics and Management, Tongji University, Shanghai 200092, China;

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