Related papers: Simplex Frank-Wolfe: Linear Convergence and Its Nu…
This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combination of smooth and non-smooth functions. To tackle these…
We propose the pivoting meta algorithm (PM) to enhance optimization algorithms that generate iterates as convex combinations of vertices of a feasible region $C\subseteq \mathbb{R}^n$, including Frank-Wolfe (FW) variants. PM guarantees that…
Nonnegative matrix factorization (NMF) often relies on the separability condition for tractable algorithm design. Separability-based NMF is mainly handled by two types of approaches, namely, greedy pursuit and convex programming. A notable…
Deep neural networks is today one of the most popular choices in classification, regression and function approximation. However, the training of such deep networks is far from trivial as there are often millions of parameters to tune.…
We propose a semi-stochastic Frank-Wolfe algorithm with away-steps for regularized empirical risk minimization and extend it to problems with block-coordinate structure. Our algorithms use adaptive step-size and we show that they converge…
The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex problems, with step sizes…
We derive a memory-efficient first-order variable splitting algorithm for convex image reconstruction problems with non-smooth regularization terms. The algorithm is based on a primal-dual approach, where one of the dual variables is…
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…
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…
We study constrained stochastic programs where the decision vector at each time slot cannot be chosen freely but is tied to the realization of an underlying random state vector. The goal is to minimize a general objective function subject…
In the paper, we propose a class of accelerated stochastic gradient-free and projection-free (a.k.a., zeroth-order Frank-Wolfe) methods to solve the constrained stochastic and finite-sum nonconvex optimization. Specifically, we propose an…
How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this…
We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal…
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,…
Minimizing a convex function over the spectrahedron, i.e., the set of all positive semidefinite matrices with unit trace, is an important optimization task with many applications in optimization, machine learning, and signal processing. It…
Projection-free optimization algorithms, which are mostly based on the classical Frank-Wolfe method, have gained significant interest in the machine learning community in recent years due to their ability to handle convex constraints that…
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…
This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…
Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a…
We present a new class of polynomial-time algorithms for submodular function minimization (SFM), as well as a unified framework to obtain strongly polynomial SFM algorithms. Our algorithms are based on simple iterative methods for the…