到最近稳定Metzler矩阵的距离
Distance to the Nearest Stable Metzler Matrix
AI总结：
研究如何找到给定不稳定矩阵最近的Metzler矩阵，并采用 dissipative Hamiltonian 理论提出块坐标下降算法，结合二次规划和半正定规划提升计算效率。
摘要：
本文考虑了寻找给定可能不稳定矩阵最近Metzler矩阵的非凸问题。线性系统其状态向量按照Metzler矩阵演化具有许多在分析和控制中关于可扩展性的良好性质。这促使问题：我们离最近的Metzler矩阵有多近（以系数的Frobenius范数）？在放弃Metzler约束的情况下，这个问题最近已使用耗散哈密顿（DH）系统理论进行研究，该理论提供了稳定矩阵可行集的有用表征。本文利用DH理论提出一种由具有有利结构性质的二次规划和半正定规划组成的块坐标下降算法，近期对角占优结果可用于提升可计算性。
英文摘要：
This paper considers the non-convex problem of finding the nearest Metzler matrix to a given possibly unstable matrix. Linear systems whose state vector evolves according to a Metzler matrix have many desirable properties in analysis and control with regard to scalability. This motivates the question, how close (in the Frobenius norm of coefficients) to the nearest Metzler matrix are we? Dropping the Metzler constraint, this problem has recently been studied using the theory of dissipative Hamiltonian (DH) systems, which provide a helpful characterization of the feasible set of stable matrices. This work uses the DH theory to provide a block coordinate descent algorithm consisting of a quadratic program with favourable structural properties and a semidefinite program for which recent diagonal dominance results can be used to improve tractability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
