Related papers: A generalized conditional gradient method for mult…
We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the…
In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when…
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…
The Frank-Wolfe (FW) method is a popular algorithm for solving large-scale convex optimization problems appearing in structured statistical learning. However, the traditional Frank-Wolfe method can only be applied when the feasible region…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a…
In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…
We investigate the resolution of second-order, potential, and monotone mean field games with the generalized conditional gradient algorithm, an extension of the Frank-Wolfe algorithm. We show that the method is equivalent to the fictitious…
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…
Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…
Solving constrained optimization problems by multi-objective evolutionary algorithms has scored tremendous achievements in the last decade. Standard multi-objective schemes usually aim at minimizing the objective function and also the…
This study proposes an airborne multisensor management algorithm for target tracking, taking each of multiple unmanned aircraft as a sensor. The purpose of the algorithm is to determine the configuration of the sensor deployment and to…
Frank-Wolfe methods (FW) have gained significant interest in the machine learning community due to its ability to efficiently solve large problems that admit a sparse structure (e.g. sparse vectors and low-rank matrices). However the…
The Frank-Wolfe algorithm is a popular method for minimizing a smooth convex function $f$ over a compact convex set $\mathcal{C}$. While many convergence results have been derived in terms of function values, hardly nothing is known about…
We consider the composite minimization problem with the objective function being the sum of a continuously differentiable and a merely lower semicontinuous and extended-valued function. The proximal gradient method is probably the most…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
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…
The Frank Wolfe algorithm (FW) is a popular projection-free alternative for solving large-scale constrained optimization problems. However, the FW algorithm suffers from a sublinear convergence rate when minimizing a smooth convex function…
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 steepest descent method for multiobjective optimization on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The aim of the paper is twofold. Firstly, an asymptotic analysis of the method is…