Tuyen Tran – Optimization Online

Clustering and Multifacility Location with Constraints via Distance Function Penalty Method and DC Programming

Published: 2017/08/04, Updated: 2018/05/02

Nonsmooth Optimization clustering, dc programming, k-mean algorithm, nesterov's smoothing techniques

This paper is a continuation of our effort in using mathematical optimization involving DC programming in clustering and multifacility location. We study a penalty method based on distance functions and apply it particularly to a number of problems in clustering and multifacility location in which the centers to be found must lie in some given … Read more

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

Published: 2016/10/17

Boris S. Mordukhovich

Nguyen Mau Nam

R. Blake Rector

Tuyen Tran

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