Jiaming Liang

Unifying restart accelerated gradient and proximal bundle methods

  • Jiaming Liang
    • Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , , , ,

    This paper presents a novel restarted version of Nesterov’s accelerated gradient method and establishes its optimal iteration-complexity for solving convex smooth composite optimization problems. The proposed restart accelerated gradient method is shown to be a specific instance of the accelerated inexact proximal point framework introduced in “An accelerated hybrid proximal extragradient method for convex optimization … Read more

    Primal-dual proximal bundle and conditional gradient methods for convex problems

  • Jiaming Liang
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , ,

    This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for solving convex nonsmooth composite optimization problems and establish the iteration-complexity in terms of a primal-dual gap. We also propose a class of proximal bundle … Read more

    Universal subgradient and proximal bundle methods for convex and strongly convex hybrid composite optimization

  • Vincent Guigues
  • Jiaming Liang
  • Renato D.C. Monteiro
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , ,

    This paper develops two parameter-free methods for solving convex and strongly convex hybrid composite optimization problems, namely, a composite subgradient type method and a proximal bundle type method. Both functional and stationary complexity bounds for the two methods are established in terms of the unknown strong convexity parameter. To the best of our knowledge, the … Read more

    Variance Reduction and Low Sample Complexity in Stochastic Optimization via Proximal Point Method

  • Jiaming Liang
    • Categories Convex Optimization, Stochastic Programming Tags , , , , ,

    This paper proposes a stochastic proximal point method to solve a stochastic convex composite optimization problem. High probability results in stochastic optimization typically hinge on restrictive assumptions on the stochastic gradient noise, for example, sub-Gaussian distributions. Assuming only weak conditions such as bounded variance of the stochastic gradient, this paper establishes a low sample complexity … Read more

    Proximal bundle methods for hybrid weakly convex composite optimization problems

  • Jiaming Liang
  • Renato D.C. Monteiro
  • Honghao Zhang
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    This paper establishes the iteration-complexity of proximal bundle methods for solving hybrid (i.e., a blend of smooth and nonsmooth) weakly convex composite optimization (HWC-CO) problems. This is done in a unified manner by considering a proximal bundle framework (PBF) based on a generic bundle update framework which includes various well-known bundle update schemes. In contrast … Read more

    A single cut proximal bundle method for stochastic convex composite optimization

  • Jiaming Liang
  • Vincent Guigues
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , , ,

    This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it. Complexity guarantees are established for them without requiring knowledge of parameters associated with the problem instance. Moreover, it is shown … Read more

    A unified analysis of a class of proximal bundle methods for solving hybrid convex composite optimization problems

  • Jiaming Liang
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    This paper presents a proximal bundle (PB) framework based on a generic bundle update scheme for solving the hybrid convex composite optimization (HCCO) problem and establishes a common iteration-complexity bound for any variant belonging to it. As a consequence, iteration-complexity bounds for three PB variants based on different bundle update schemes are obtained in the … Read more

    Average Curvature FISTA for Nonconvex Smooth Composite Optimization Problems

  • Jiaming Liang
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    A previous authors’ paper introduces an accelerated composite gradient (ACG) variant, namely AC-ACG, for solving nonconvex smooth composite optimization (N-SCO) problems. In contrast to other ACG variants, AC-ACG estimates the local upper curvature of the N-SCO problem by using the average of the observed upper-Lipschitz curvatures obtained during the previous iterations, and uses this estimation … Read more

    A proximal bundle variant with optimal iteration-complexity for a large range of prox stepsizes

  • Jiaming Liang
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    This paper presents a proximal bundle variant, namely, the relaxed proximal bundle (RPB) method, for solving convex nonsmooth composite optimization problems. Like other proximal bundle variants, RPB solves a sequence of prox bundle subproblems whose objective functions are regularized composite cutting-plane models. Moreover, RPB uses a novel condition to decide whether to perform a serious … Read more

    An Average Curvature Accelerated Composite Gradient Method for Nonconvex Smooth Composite Optimization Problems

  • Jiaming Liang
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth composite minimization problems. As opposed to well-known ACG variants that are either based on a known Lipschitz gradient constant or a sequence of maximum observed curvatures, the current one is based on a sequence of average … Read more