Cui Zengru, Yuan Gonglin, Sheng Zhou, Liu Wenjie, Wang Xiaoliang, Duan Xiabin
Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China.
Guangxi Colleges and Universities Key Laboratory of Mathematics and Its Applications, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China; School of Computer and Software, Nanjing University of Information Science & Technology, Nanjing 210044, China.
PLoS One. 2015 Oct 26;10(10):e0140606. doi: 10.1371/journal.pone.0140606. eCollection 2015.
This paper proposes a modified BFGS formula using a trust region model for solving nonsmooth 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.
本文提出了一种改进的BFGS公式，该公式使用信赖域模型，通过莫罗-约西达正则化（平滑）方法和带有BFGS更新公式的新割线方程来求解非光滑凸极小化问题。我们的算法利用函数值信息和梯度值信息来计算海森矩阵。海森矩阵通过BFGS公式更新，而不是使用函数的二阶信息，从而减少了计算中的工作量和时间。在适当条件下，该算法全局收敛到最优解。数值结果表明，该算法能够成功地解决非光滑无约束凸问题。
