LMI优化的一种原对偶中心路径算法

A Primal-Dual Central Path Algorithm for LMI Optimization

系统和控制理论中许多重要的问题,都可转化为具有线性目标函数、线性矩阵不等式约束的LMI优化问题,从而使其在数值上易于求解.本文给出一种求解LMI优化问题的原对偶中心路径算法,该算法利用牛顿方法求解中心路径方程得到牛顿系统,并将该牛顿系统对称化以避免得到非对称化的搜索方向.文章详细分析了算法的计算复杂性.

A number of important problems from system and control theory can be numerically solved by reformulating them as LMI optimization problems, i.e., minimization of a linear objective subject to linear matrix inequality constraints. The primary purpose of this article is to provide a primal-dual central path algorithm for LMI optimization. The algorithm apply Newton＇s method to a primal-dual central path equations to obtain a Newton system which is then symmetrized to avoid nonsymmetric search direction. Polynomial convergence results are derived in detail.