A Bundle Trust Region Algorithm for Minimizing Locally Lipschitz Functions
提出一种结合束方法与信赖域技术的新算法，用于最小化局部Lipschitz函数，在较低光滑性假设下证明全局收敛，数值实验表明对非光滑非凸问题有效。
.We propose a new algorithm for minimizing locally Lipschitz functions that combines both the bundle and trust region techniques. Based on the bundle methods the objective function is approximated by a piecewise linear working model which is updated by adding cutting planes at unsuccessful trial steps. The algorithm defines, at each iteration, a new trial point by solving a subproblem that employs the working model in the objective function subject to a region, which is called the trust region. The algorithm is studied from both theoretical and practical points of view. Under a \(\textrm{lower-}C^{1}\) assumption on the objective function, global convergence of it is verified to stationary points. In order to demonstrate the reliability and efficiency of the proposed algorithm, a MATLAB implementation of it is prepared and numerical experiments have been made using some academic nonsmooth test problems. Computational results show that the developed method is efficient for solving nonsmooth and nonconvex optimization problems.Keywordsnonsmooth and nonconvex optimizationtrust region methodbundle algorithmMSC codes90C2649J5265K05