Related papers: The Frank-Wolfe algorithm: a short introduction
The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space…
The paper presents various modifications of the Frank-Wolfe algorithm in the equilibrium traffic assignment problem. The Beckman model is used as a model for experiments. In this article, first of all, attention is paid to the choice of the…
Projection-free optimization via different variants of the Frank-Wolfe (FW) method has become one of the cornerstones in large scale optimization for machine learning and computational statistics. Numerous applications within these fields…
We investigate the robustness of the Frank-Wolfe method when gradients are computed inexactly and examine the relative computational cost of the linear minimization oracle (LMO) versus projection. For smooth nonconvex functions, we…
Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers such as Lion and Muon have gained quite significant popularity in deep learning. In this work,…
In constrained convex optimization, existing methods based on the ellipsoid or cutting plane method do not scale well with the dimension of the ambient space. Alternative approaches such as Projected Gradient Descent only provide a…
Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of…
We discuss the problem of projecting a point onto an arbitrary hyperbolicity cone from both theoretical and numerical perspectives. While hyperbolicity cones are furnished with a generalization of the notion of eigenvalues, obtaining closed…
Two of the most fundamental prototypes of greedy optimization are the matching pursuit and Frank-Wolfe algorithms. In this paper, we take a unified view on both classes of methods, leading to the first explicit convergence rates of matching…
In the first part of this dissertation research, we develop a modular framework that can serve as a recipe for constructing and analyzing iterative algorithms for convex optimization. Specifically, our work casts optimization as iteratively…
The optimal transport (OT) problem has been used widely for machine learning. It is necessary for computation of an OT problem to solve linear programming with tight mass-conservation constraints. These constraints prevent its application…
We consider two greedy algorithms for minimizing a convex function in a bounded convex set: an algorithm by Jones [1992] and the Frank-Wolfe (FW) algorithm. We first consider approximate versions of these algorithms. For smooth convex…
With increasingly "big" data available in biomedical research, deriving accurate and reproducible biology knowledge from such big data imposes enormous computational challenges. In this paper, motivated by recently developed stochastic…
This paper proposes a distributed stochastic projection-free algorithm for large-scale constrained finite-sum optimization whose constraint set is complicated such that the projection onto the constraint set can be expensive. The global…
Optimization problems under affine constraints appear in various areas of machine learning. We consider the task of minimizing a smooth strongly convex function F(x) under the affine constraint Kx=b, with an oracle providing evaluations of…
In recent years it was proved that simple modifications of the classical Frank-Wolfe algorithm (aka conditional gradient algorithm) for smooth convex minimization over convex and compact polytopes, converge with linear rate, assuming the…
This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or…
Structured constraints in Machine Learning have recently brought the Frank-Wolfe (FW) family of algorithms back in the spotlight. While the classical FW algorithm has poor local convergence properties, the Away-steps and Pairwise FW…
Aiming at convex optimization under structural constraints, this work introduces and analyzes a variant of the Frank Wolfe (FW) algorithm termed ExtraFW. The distinct feature of ExtraFW is the pair of gradients leveraged per iteration,…
Metarounding is an approach to convert an approximation algorithm for linear optimization over some combinatorial classes to an online linear optimization algorithm for the same class. We propose a new metarounding algorithm under a natural…