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This paper considers continuous-time coordination algorithms for networks of agents that seek to collectively solve a general class of nonsmooth convex optimization problems with an inherent distributed structure. Our algorithm design…
We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight…
Recent applications in machine learning have renewed the interest of the community in min-max optimization problems. While gradient-based optimization methods are widely used to solve such problems, there are however many scenarios where…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
The generalized conditional gradient method is a popular algorithm for solving composite problems whose objective function is the sum of a smooth function and a nonsmooth convex function. Many convergence analyses of the algorithm rely on…
We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap…
In this paper, we present a novel Newton-based extremum seeking controller for the solution of multivariable model-free optimization problems in static maps. Unlike existing asymptotic and fixed-time results in the literature, we present a…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While…
We propose a first-order method for solving inequality constrained optimization problems. The method is derived from our previous work [12], a modified search direction method (MSDM) that applies the singular-value decomposition of…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
A fundamental class of matrix optimization problems that arise in many areas of science and engineering is that of quadratic optimization with orthogonality constraints. Such problems can be solved using line-search methods on the Stiefel…
Minimization methods that search along a curvilinear path composed of a non-ascent nega- tive curvature direction in addition to the direction of steepest descent, dating back to the late 1970s, have been an effective approach to finding a…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings --…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…