We show the linear convergence of a simple first-order algorithm for the minimum-volume enclosing ellipsoid problem and its dual, the D-optimal design problem of statistics. Computational tests confirm the attractive features of this method.

Mixed-Integer optimization is a powerful tool for modeling many optimization problems arising from real-world applications. Finding a first feasible solution represents the first step for several MIP solvers. The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems which is effective even when dealing with hard MIP instances. In this work, we start by ...

We give a detailed proof, under slightly weaker conditions on the objective function, that a modified Frank-Wolfe algorithm based on Wolfe's "away step" strategy can achieve geometric convergence, provided a strict complementarity assumption holds.

We study the problem of privacy-preserving collaborative filtering where the objective is to reconstruct the entire users-items preference matrix using a few observed preferences of users for some of the items. Furthermore, the collaborative filtering algorithm should reconstruct the preference matrix while preserving the privacy of each user. We study this problem in the setting of joint diffe...

This paper considers distributed stochastic optimization, in which a number of agents cooperate to optimize global objective function through local computations and information exchanges with neighbors over network. Stochastic optimization problems are usually tackled by variants projected gradient descent. However, projecting point onto feasible set is often expensive. The Frank-Wolfe (FW) met...

Abstract We present and analyze a new generalized Frank–Wolfe method for the composite optimization problem $$(P): {\min }_{x\in {\mathbb {R}}^n} \; f(\mathsf {A} x) + h(x)$$ ( P ) : min x ∈</mml...

The Frank-Wolfe algorithm is a method for constrained optimization relying on linear minimizations, as opposed to projections. Therefore, motivation put forward in large body of work the computational advantage solving minimizations instead However, discussions supporting this are often incomplete. We review complexity bounds both tasks several sets commonly used optimization. Projection method...

We propose a randomized block-coordinate variant of the classic Frank-Wolfe algorithm for convex optimization with block-separable constraints. Despite its lower iteration cost, we show that it achieves a similar convergence rate in duality gap as the full FrankWolfe algorithm. We also show that, when applied to the dual structural support vector machine (SVM) objective, this yields an online a...