Quoc Tran-Dinh

A Primal-Dual Algorithmic Framework for Constrained Convex Minimization

  • Volkan Cevher
  • Quoc Tran-Dinh
    • Categories Convex and Nonsmooth Optimization

    We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our main analysis technique provides a fresh perspective on Nesterov’s excessive gap technique in a structured fashion and unifies it with smoothing and primal-dual methods. For instance, … Read more

    An inexact proximal path-following algorithm for constrained convex minimization

  • Volkan Cevher
  • Quoc Tran-Dinh
  • Anastasios Kyrillidis
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a tractable proximity operator and that the convex constraints afford a self-concordant barrier. We provide a new joint treatment … Read more

    Composite Self-concordant Minimization

  • Volkan Cevher
  • Quoc Tran-Dinh
  • Anastasios Kyrillidis
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Statistics Tags , , , ,

    We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function endowed with a computable proximal operator. We theoretically establish the convergence of our framework without relying on the usual Lipschitz gradient assumption on the smooth part. An important highlight of our work is a new … Read more

    COMPUTATIONAL COMPLEXITY OF INEXACT GRADIENT AUGMENTED LAGRANGIAN METHODS: APPLICATION TO CONSTRAINED MPC

  • Ion Necoara
  • Quoc Tran-Dinh
  • Valentin Nedelcu
    • Categories Control Applications, Convex and Nonsmooth Optimization, Convex Optimization Tags , , , , ,

    We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the relaxation of complicating constraints with gradient and fast gradient methods based on inexact first order information. Moreover, since the exact solution of the augmented … Read more

    AN INEXACT PERTURBED PATH-FOLLOWING METHOD FOR LAGRANGIAN DECOMPOSITION IN LARGE-SCALE SEPARABLE CONVEX OPTIMIZATION

  • Moritz Diehl
  • Ion Necoara
  • Carlo Savorgnan
  • Quoc Tran-Dinh
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Parallel Algorithms Tags , , , , ,

    This paper studies an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale separable convex programming problems. Unlike the exact versions considered in the literature, we propose to solve the primal subproblems inexactly up to a given accuracy. This leads to an inexactness of the gradient vector and the Hessian … Read more