We propose an inexact variable-metric proximal point algorithm to accelerate gradient-based optimization algorithms. The proposed scheme, called QNing, can notably be applied to incremental first-order methods such as the stochastic variance-reduced gradient descent algorithm and other randomized incremental optimization algorithms. QNing is also compatible with composite objectives, meaning that it has the ability to provide exactly sparse solutions when the objective involves a sparsity-inducing regularization. When combined with limited-memory BFGS rules, QNing is particularly effective at solving high-dimensional optimization problems while enjoying a worst-case linear convergence rate for strongly convex problems. We present experimental results where QNing gives significant improvements over competing methods for training machine learning methods on large samples and in high dimensions.


  1. convex optimization
  2. quasi-Newton
  3. L-BFGS

MSC codes

  1. 90C25
  2. 90C53

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Information & Authors


Published In

cover image SIAM Journal on Optimization
SIAM Journal on Optimization
Pages: 1408 - 1443
ISSN (online): 1095-7189


Submitted: 10 April 2017
Accepted: 22 January 2019
Published online: 28 May 2019


  1. convex optimization
  2. quasi-Newton
  3. L-BFGS

MSC codes

  1. 90C25
  2. 90C53



Funding Information

Agence Nationale de la Recherche https://doi.org/10.13039/501100001665 : ANR-14-CE23-0003-01
Canadian Institute for Advanced Research https://doi.org/10.13039/100007631
H2020 European Research Council https://doi.org/10.13039/100010663 : 714381

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