Sparse Approximations with Interior Point Methods

doi:10.1137/21M1401103

Sparse Approximations with Interior Point Methods

2022-11-03

5

OA

AI

V

Valentina De Simone *

Spyridon Pougkakiotis

M

Marco Viola

DOI：10.1137/21M1401103

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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.

Keywords:

sparse approximations

interior point methods

proximal methods of multipliers

nonlinear convex programming

solution of KKT systems

portfolio optimization

image restoration

classification in machine learning

Sparse Approximations with Interior Point Methods

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