Nguyen Thai An

VARIATIONAL INEQUALITIES GOVERNED BY STRONGLY PSEUDOMONOTONE VECTOR FIELDS ON HADAMARD MANIFOLDS

  • Nguyen Thai An
  • Luong Nguyen
  • Nguyen Thu
    • Categories Complementarity and Variational Inequalities Tags , , , , ,

    We consider variational inequalities governed by strongly pseudomonotone vec- tor fields on Hadamard manifolds. The existence and uniqueness results of the solution, linear convergence, error estimates and finite convergence for sequences generated by a mod- ified projection method for solving variational inequalities are investigated. Some examples and numerical experiments are also given to illustrate our … Read more

    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. ArticleDownload View PDF

    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

    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