Non accelerated efficient numerical methods for sparse quadratic optimization problems and its generalizations

TL;DR

This paper compares non-accelerated primal gradient and conditional gradient methods for sparse quadratic optimization, showing they can outperform accelerated methods in certain cases and exploring their generalizations.

Contribution

It demonstrates that non-accelerated primal and conditional gradient methods can be more effective than accelerated approaches for specific sparse quadratic problems and discusses their extensions.

Findings

Non-accelerated methods can outperform accelerated ones in some sparse quadratic cases

Primal gradient and conditional gradient methods are effective for certain problem classes

The paper explores generalizations of these methods

Abstract

We investigate primal gradient method with l1-norm and conditional gradient method (both methods are non accelerated). We show that these methods can outperform well known accelerated approaches for some classes of sparse quadratic problems. Moreover we discuss some generalizations.