An Approximate Redistributed Proximal Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions
Jie Shen, Xiaoqian Liu, Fangfang Guo, Shuxin Wang · Mathematical Problems in Engineering · 2015
We describe an extension of the redistributed technique form classical proximal bundle method to the inexact situation for minimizing nonsmooth nonconvex functions. The cutting-planes model we construct is not the approximation to the whole nonconvex function, but to the local convexification of the approximate objective function, and this kind of local convexification is modified dynamically in order to always yield nonnegative linearization errors. Since we only employ the approximate function values and approximate subgradients, theoretical convergence analysis shows that an approximate stationary point or some double approximate stationary point can be obtained under some mild conditions.