# Numerical Analysis and Scientific Computing Seminar

## On the Linear Convergence of the Frank-Wolfe Algorithm

**Speaker:**
Javier Pena, Carnegie Mellon University

**Location:**
Warren Weaver Hall 1302

**Date:**
Sept. 9, 2016, 10 a.m.

**Synopsis:**

The Frank-Wolfe algorithm, also known as the conditional gradient algorithm, is a first-order algorithm to minimize a convex function over a convex set. The algorithm relies only on a gradient oracle for the objective function and a linear oracle for the constraint set. This algorithm was introduced in the 1950s and it has had a remarkable surge in popularity in the last few years. The algorithm is especially well-suited to generate parsimonious solutions to large-scale optimization problems.

This talk will describe the Frank-Wolfe algorithm and some of its variants. We will place special emphasis on recent results related to the linear convergence of the algorithm when the objective function is strongly convex with Lipschitz gradient and the constraint set is a polytope. In this case the main linear convergence statement is an elegant generalization of the analogous linear convergence property of the gradient descent method for unconstrained convex minimization.

This talk is based on joint work with Daniel Rodriguez, Department of Mathematical Sciences, Carnegie Mellon University.