一类张量特征值互补问题的分式规划等价形式

An Equivalent Fractional Programming Form of a Class of Tensor Eigenvalue Complementarity Problems

提出了一类与非线性微分包含问题密切相关的张量高次特征值互补问题。研究了此类张量高次特征值互补问题与一类齐次多项式分式规划的等价关系,为进一步设计算法提供了一条有效途径。在此基础上,得到了一个关于张量高次特征值互补问题解的存在性结果。

This paper proposes a class of tensor higher-degree eigenvalue complementarity problems, which have closely relationship with a class of nonlinear differential inclusion problems. The equivalent connection between the considered tensor higher-degree eigenvalue complementarity problems and the corresponding homogeneous polynomial fractional programming is studied, which provides an effective method for the design of the related algorithms. Based upon this, a result on existence of solution for tensor eigenvalue complementarity problems is proved.