几种特殊矩阵的Pareto特征值问题

The Pareto Eigenvalue Problem of Some Matrices

Pareto特征值问题是定义在正卦限上一类锥约束问题,在许多领域有着深厚的背景。将讨论Pareto特征值的一些理论性质,包括给定矩阵Pareto特征值范围及个数上界。引进了一类新矩阵,讨论并给出它的部分理论性质,可直接计算其最大Pareto特征值。

The Pareto eigenvaluc problem（PEP） is an important prototype of cone-constrained problems, which exhibits already many of mathematical difficulties arising in the context of complementarity conditions involving the positive orthant. In this paper, we discuss some theoretical issues such as, the bound of Pareto eigenvalues for given matrices. A new kind of matrix is introduced and analyzed, namely, Q-matrix, whose largest Pareto eigenvalue can be estimated.