FASTER LAGRANGIAN-BASED METHODS IN CONVEX OPTIMIZATION

Shoham Sabach, Marc Teboulle

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

In this paper, we aim at unifying, simplifying, and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce the notion of nice primal algorithmic map, which plays a central role in the unification and in the simplification of the analysis of most Lagrangian-based methods. Equipped with a nice primal algorithmic map, we then introduce a versatile generic scheme, which allows for the design and analysis of faster Lagrangian (FLAG) methods with new provably sublinear rate of convergence expressed in terms of function values and feasibility violation of the original (nonergodic) generated sequence. To demonstrate the power and versatility of our approach and results, we show that most well-known iconic Lagrangian-based schemes admit a nice primal algorithmic map and hence share the new faster rate of convergence results within their corresponding FLAG.

Original languageEnglish
Pages (from-to)204-227
Number of pages24
JournalSIAM Journal on Optimization
Volume32
Issue number1
DOIs
StatePublished - 2022

Funding

FundersFunder number
Israel Science Foundation2619-20, 1844-16

    Keywords

    • Lagrangian multiplier methods
    • alternating direction method of multiplier
    • augmented Lagrangian
    • convex composite minimization
    • fast nonergodic global rate of convergence
    • nonsmooth optimization
    • proximal multiplier algorithms

    Fingerprint

    Dive into the research topics of 'FASTER LAGRANGIAN-BASED METHODS IN CONVEX OPTIMIZATION'. Together they form a unique fingerprint.

    Cite this