A Modified BFGS Formula Using a Trust Region Model for Nonsmooth Convex Minimizations

作者：Cui, Zengru; Yuan, Gonglin^*; Sheng, Zhou; Liu, Wenjie; Wang, Xiaoliang; Duan, Xiabin

来源：PLos One, 2015, 10(10): e0140606.

DOI：10.1371/journal.pone.0140606

• QUASI-NEWTON METHODS
• CONVERGENCE ANALYSIS
• BUNDLE METHOD
• ALGORITHM
• SEGMENTATION
• SEARCH

This paper proposes a modified BFGS formula using a trust region model for solving non-smooth convex minimizations by using the Moreau-Yosida regularization (smoothing) approach and a new secant equation with a BFGS update formula. Our algorithm uses the function value information and gradient value information to compute the Hessian. The Hessian matrix is updated by the BFGS formula rather than using second-order information of the function, thus decreasing the workload and time involved in the computation. Under suitable conditions, the algorithm converges globally to an optimal solution. Numerical results show that this algorithm can successfully solve nonsmooth unconstrained convex problems.

• 出版日期2015-10-26
• 单位南京信息工程大学; 广西大学