Renato D.C. Monteiro

An Adaptive Proximal ADMM for Nonconvex Linearly-Constrained Composite Programs

  • Leandro Farias Maia
  • David H. Gutman
  • Renato D.C. Monteiro
  • Gilson Silva
    • Categories Convex and Nonsmooth Optimization, Global Optimization Theory, Nonlinear Optimization Tags , , , ,

    This paper develops an adaptive Proximal Alternating Direction Method of Multipliers (P-ADMM) for solving linearly-constrained, weakly convex, composite optimization problems. This method is adaptive to all problem parameters, including smoothness and weak convexity constants. It is assumed that the smooth component of the objective is weakly convex and possibly nonseparable, while the non-smooth component is … Read more

    A low-rank augmented Lagrangian method for large-scale semidefinite programming based on a hybrid convex-nonconvex approach

  • Renato D.C. Monteiro
  • Arnesh Sujanani
  • Diego Cifuentes
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , , ,

    \(\) This paper introduces HALLaR, a new first-order method for solving large-scale semidefinite programs (SDPs) with bounded domain. HALLaR is an inexact augmented Lagrangian (AL) method where the AL subproblems are solved by a novel hybrid low-rank (HLR) method. The recipe behind HLR is based on two key ingredients: 1) an adaptive inexact proximal point … Read more

    Proximal bundle methods for hybrid weakly convex composite optimization problems

  • Jiaming Liang
  • Renato D.C. Monteiro
  • HonghaoZhang
    • 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 scheme which includes various well-known bundle update schemes. In contrast … Read more

    An adaptive superfast inexact proximal augmented Lagrangian method for smooth nonconvex composite optimization problems

  • Arnesh Sujanani
  • Renato D.C. Monteiro
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex proximal augmented Lagrangian (AL) subproblem obtained by an aggressive/adaptive choice of prox stepsize with the aim of substantially improving its computational performance followed by a full Lagrangian … 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

    Global Complexity Bound of a Proximal ADMM for Linearly-Constrained Nonseperable Nonconvex Composite Programming

  • Weiwei Kong
  • Renato D.C. Monteiro
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable. Each iteration of DP.ADMM consists of: (ii) a sequence of partial proximal augmented Lagrangian (AL) updates, (ii) an under-relaxed Lagrange multiplier update, and (iii) a … Read more

    An Accelerated Inexact Dampened Augmented Lagrangian Method for Linearly-Constrained Nonconvex Composite Optimization Problems

  • Weiwei Kong
  • Renato D.C. Monteiro
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL method consists of: (i) inexactly solving a dampened proximal augmented Lagrangian (AL) subproblem by calling an accelerated composite gradient (ACG) subroutine; (ii) applying a dampened and under-relaxed Lagrange multiplier update; … 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

    FISTA and Extensions – Review and New Insights

  • Weiwei Kong
  • Jefferson Gonçalves Melo
  • Renato D.C. Monteiro
    • Categories Convex Optimization, Nonsmooth Optimization Tags , ,

    The purpose of this technical report is to review the main properties of an accelerated composite gradient (ACG) method commonly referred to as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). In addition, we state a version of FISTA for solving both convex and strongly convex composite minimization problems and derive its iteration complexities to generate iterates … 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