Bundle-type methods for inexact data

We treat such convex programming problems, the constraints and objective functions of which are not easy to handle: the more accurate data we want, the greater the computational effort. We propose such bundle-type methods that keep balance between the amount of work invested into estimating the function data on the one hand, and into the optimization method on the other hand. At the beginning, only rough estimates of the function values and gradients are needed. As the optimum is gradually approached, more and more accurate data are computed. The proposed methods inherit stability from bundle methods, moreover, the functions need not be smooth.