Simplified Versions of the Conditional Gradient Method

TL;DR

This paper introduces simplified modifications to the conditional gradient method that preserve convergence while reducing implementation complexity and computational costs, demonstrated through preliminary computational tests.

Contribution

The paper presents new step-size and inexact subproblem solutions for the conditional gradient method, enhancing efficiency without sacrificing convergence properties.

Findings

Reduced iteration cost through inexact subproblem solutions

Elimination of line-search in step-size determination

Preliminary computational tests confirm efficiency improvements

Abstract

We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the step-size procedure without any line-search, and inexact solution of the direction finding subproblem. Preliminary results of computational tests confirm efficiency of the proposed modifications.