A Filter Active-Set Algorithm for Ball/Sphere Constrained Optimization Problem
提出一种过滤积极集算法，利用球/球面约束的稀疏结构设计L-BFGS方案，求解多球/球面约束的最小化问题，在相关矩阵和最大相关问题上表现优于定制方法。
In this paper, we propose a filter active-set algorithm for the minimization problem over a product of multiple ball/sphere constraints. By making effective use of the special structure of the ball/sphere constraints, a new limited memory BFGS (L-BFGS) scheme is presented. The new L-BFGS implementation takes advantage of the sparse structure of the Jacobian of the constraints and generates curvature information of the minimization problem. At each iteration, only two or three reduced linear systems are required to solve for the search direction. The filter technique combined with the backtracking line search strategy ensures the global convergence, and the local superlinear convergence can also be established under mild conditions. The algorithm is applied to two specific applications, the nearest correlation matrix with factor structure and the maximal correlation problem. Our numerical experiments indicate that the proposed algorithm is competitive with some recently custom-designed methods for each individual application.