Nguyen Mau Nam

Characterizations of Differentiability, Smoothing Techniques and DC Programming with Applications to Image Reconstructions

  • Nguyen Thai An
  • Le Thi Hoai An
  • Daniel Giles
  • Nguyen Mau Nam
    • Categories Convex and Nonsmooth Optimization

    In this paper, we study characterizations of differentiability for real-valued functions based on generalized differentiation. These characterizations provide the mathematical foundation for Nesterov’s smoothing techniques in infinite dimensions. As an application, we provide a simple approach to image reconstructions based on Nesterov’s smoothing techniques and DC programming that involves the $\ell_1-\ell_2$ regularization. Article Download View … Read more

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

  • Nguyen Thai An
  • Nguyen Mau Nam
  • Sam Reynolds
  • Tuyen Tran
    • Categories Nonsmooth Optimization Tags , , ,

    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

  • Boris S. Mordukhovich
  • Nguyen Mau Nam
  • R. Blake Rector
  • Tuyen Tran
    • Categories Convex and Nonsmooth Optimization Tags , , , , ,

    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 uni ed and simplified proofs based on the developed … Read more

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

  • Nguyen Thai An
  • Jie Sun
  • Nguyen Mau Nam
  • R. Blake Rector
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    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 nondi erentiabilty of the distance functions therein. Another approach involves approximating nonsmooth optimization problems by smooth optimizations problems using Nesterov’s smoothing techniques. Convergence … Read more

    Partial Second-Order Subdifferentials in Variational Analysis and Optimization

  • Boris S. Mordukhovich
  • Nguyen Mau Nam
  • Nguyen Thi Yen Nhi
    • Categories Nonsmooth Optimization Tags , , , , , ,

    This paper presents a systematic study of partial second-order subdifferentials for extended-real-valued functions, which have already been applied to important issues of variational analysis and constrained optimization in finite-dimensional spaces. The main results concern developing extended calculus rules for these second-order constructions in both finite-dimensional and infinite-dimensional frameworks. We also provide new applications of partial … Read more