Sparse Approximations with Interior Point Methods

Valentina De Simone, Daniela di Serafino, Jacek Gondzio, Spyridon Pougkakiotis, Marco Viola

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
27 Downloads (Pure)

Abstract

Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well-conditioned problems. In this paper, specialized variants of an interior point-proximal method of multipliers are proposed and analyzed for problems of this class. Computational experience on a variety of problems, namely, multiperiod portfolio optimization, classification of data coming from functional magnetic resonance imaging, restoration of images corrupted by Poisson noise, and classification via regularized logistic regression, provides substantial evidence that interior point methods, equipped with suitable linear algebra, can offer a noticeable advantage over first-order approaches.

Original languageEnglish
Pages (from-to)954-988
Number of pages35
JournalSIAM Review
Volume64
Issue number4
Early online date3 Nov 2022
DOIs
Publication statusPublished - Nov 2022

Keywords

  • classification in machine learning
  • image restoration
  • interior point methods
  • nonlinear convex programming
  • portfolio optimization
  • proximal methods of multipliers
  • solution of KKT systems
  • sparse approximations

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics

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