Related papers: Composite convex minimization involving self-conco…
In this article, we propose a new approach, optimize then agree for minimizing a sum $ f = \sum_{i=1}^n f_i(x)$ of convex objective functions over a directed graph. The optimize then agree approach decouples the optimization step and the…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
We consider the general problem of minimizing an objective function which is the sum of a convex function (not strictly convex) and absolute values of a subset of variables (or equivalently the l1-norm of the variables). This problem…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…
We present a unified theorem for the convergence analysis of stochastic gradient algorithms for minimizing a smooth and convex loss plus a convex regularizer. We do this by extending the unified analysis of Gorbunov, Hanzely \& Richt\'arik…
In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…
The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…
In this paper, we present a conditional gradient type (CGT) method for solving a class of composite optimization problems where the objective function consists of a (weakly) smooth term and a (strongly) convex regularization term. While…
We analyze the constant step size subgradient method on nonsmooth, nonconvex functions. We identify geometric assumptions on the objective function under which i) its domain admits a partition (stratification) into smooth manifolds (strata)…
We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs…
The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex…
We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…
We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
Some variant of the Frank-Wolfe method for convex optimization problems with adaptive selection of the step parameter corresponding to information about the smoothness of the objective function (the Lipschitz constant of the gradient).…
Optimization of convex functions under stochastic zeroth-order feedback has been a major and challenging question in online learning. In this work, we consider the problem of optimizing second-order smooth and strongly convex functions…