Minimization of the Sum of Minima of Convex Functions and Its Application to Clustering

Abstract

We study functions that can be represented as the sum of minima of convex functions. Minimization of such functions can be used for approximation of finite sets and their clustering. We suggest to use the local discrete gradient (DG) method [1] and the hybrid method between the cutting angle method and the discrete gradient method (DG+CAM) [5] for the minimization of these functions. We report and analyze the results of numerical experiments.