求解一类二次矩阵优化问题的BFGS方法

The BFGS method for solving a class of quadratic matrix optimization problem

针对一类矩阵优化问题,提出了一种基于Armijo搜索准则的快速收敛的迭代算法。利用半正定矩阵的Gramian表示,将该问题转化为无约束优化问题,并设计BFGS方法来求解等价问题。数值例子验证了新方法的可行性。

Aiming at a class of quadratic matrix optimization problem,a fast convergent iterative algorithm based on Armijo line search is proposed.Using the Gramian representation of a positive semidefinite matrix,the problem is transformed into an unconstrained optimization problem,and BFGS method is used to solve the equivalent problem.Numerical experiments illustrate the feasibility of the new method.