R. Blake Rector – Optimization Online

Variational Geometric Approach to Generalized Differential and Fenchel Conjugate Calculi in Convex Analysis

Published: 2016/10/17

Convex and Nonsmooth Optimization coderivatives, convex and variational analysis, convex calculus, fenchel conjugates, normals and subgradients, optimal value functions

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unied and simplified proofs based on the developed … Read more

Nonsmooth Algorithms and Nesterov’s Smoothing Techniques for Generalized Fermat-Torricelli Problems

Published: 2013/07/22, Updated: 2014/05/07

Convex and Nonsmooth Optimization generalized fermat-torricelli problem, mm principle, nesterov's accelerated gradient method, subgradient-type algorithms

In this paper we present some algorithms for solving a number of new models of facility location involving sets which generalize the classical Fermat-Torricelli problem. Our approach uses subgradient-type algorithms to cope with nondierentiabilty of the distance functions therein. Another approach involves approximating nonsmooth optimization problems by smooth optimizations problems using Nesterov’s smoothing techniques. Convergence … Read more