Related papers: The Pivoting Framework: Frank-Wolfe Algorithms wit…
Similarity and metric learning provides a principled approach to construct a task-specific similarity from weakly supervised data. However, these methods are subject to the curse of dimensionality: as the number of features grows large,…
We consider the oracle complexity of constrained convex optimization given access to a Linear Minimization Oracle (LMO) for the constraint set and a gradient oracle for the $L$-smooth, strongly convex objective. This model includes…
The Frank-Wolfe algorithm has become a popular first-order optimization algorithm for it is simple and projection-free, and it has been successfully applied to a variety of real-world problems. Its main drawback however lies in its…
We propose a primal heuristic for quadratic mixed-integer problems. Our method extends the Boscia framework -- originally a mixed-integer convex solver leveraging a Frank-Wolfe-based branch-and-bound approach -- to address nonconvex…
In this paper, we consider large-scale linearly constrained composite convex optimization problem, whose objective is a sum of a smooth function and a possibly nonsmooth function. We propose a scalable \textbf{F}rank-\textbf{W}olfe based…
We consider minimizing $f(x) = \mathbb{E}[f(x,\omega)]$ when $f(x,\omega)$ is possibly nonsmooth and either strongly convex or convex in $x$. (I) Strongly convex. When $f(x,\omega)$ is $\mu-$strongly convex in $x$, we propose a variable…
We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…
We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers…
This work proposes a new algorithm for training a re-weighted L2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Cand\`es et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In…
In this paper, we consider Frank-Wolfe-based algorithms for composite convex optimization problems with objective involving a logarithmically-homogeneous, self-concordant functions. Recent Frank-Wolfe-based methods for this class of…
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 present new results for the Frank-Wolfe method (also known as the conditional gradient method). We derive computational guarantees for arbitrary step-size sequences, which are then applied to various step-size rules, including simple…
We study projection-free methods for constrained Riemannian optimization. In particular, we propose the Riemannian Frank-Wolfe (RFW) method. We analyze non-asymptotic convergence rates of RFW to an optimum for (geodesically) convex…
This work studies and develop projection-free algorithms for online learning with linear optimization oracles (a.k.a. Frank-Wolfe) for handling the constraint set. More precisely, this work (i) provides an improved (optimized) variant of an…
It is known that the gradient descent algorithm converges linearly when applied to a strongly convex function with Lipschitz gradient. In this case the algorithm's rate of convergence is determined by the condition number of the function.…
Nous nous int\'eressons \`a la reconstruction parcimonieuse d'images \`a l'aide du probl\`eme d'optimisation r\'egularis\'e LASSO. Dans de nombreuses applications pratiques, les grandes dimensions des objets \`a reconstruire limitent, voire…
Curvature properties of convex objects, such as strong convexity, are important in designing and analyzing convex optimization algorithms in the Hilbertian or Riemannian settings. In the case of the Hilbertian setting, strongly convex sets…
Optimal transport (OT), which provides a distance between two probability distributions by considering their spatial locations, has been applied to widely diverse applications. Computing an OT problem requires solution of linear programming…
Recent work has shown that in certain settings, the Frank-Wolfe algorithm (FW) with open-loop step-sizes $\eta_t = \frac{\ell}{t+\ell}$ for a fixed parameter $\ell \in \mathbb{N},\, \ell \geq 2$, attains a convergence rate faster than the…
The control of large buildings encounters challenges in computational efficiency due to their size and nonlinear components. To address these issues, this paper proposes a Piecewise Affine (PWA)-based distributed scheme for Model Predictive…