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We consider minimizing an objective function subject to constraints defined by the intersection of lower-level sets of convex functions. We study two cases: (i) strongly convex and Lipschitz-smooth objective function and (ii) convex but…
In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems. We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation…
Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
We introduce an extension of the Difference of Convex Algorithm (DCA) in the form of a randomized block coordinate approach for problems with separable structure. For $n$ coordinate-blocks and $k$ iterations, our main result proves a…
This paper presents a family of algorithms for decentralized convex composite problems. We consider the setting of a network of agents that cooperatively minimize a global objective function composed of a sum of local functions plus a…
Typically, the sequence of points generated by an optimization algorithm may have multiple limit points. Under convexity assumptions, however, (sub)gradient methods are known to generate a convergent sequence of points. In this paper, we…
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…
We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is…
Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…
This paper presents a decentralized algorithm for a team of agents to track time-varying fixed points that are the solutions to time-varying convex optimization problems. The algorithm is first-order, and it allows for total asynchrony in…
In this paper, we develop two new randomized block-coordinate optimistic gradient algorithms to approximate a solution of nonlinear equations in large-scale settings, which are called root-finding problems. Our first algorithm is…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number…
In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
We consider unconstrained randomized optimization of convex objective functions. We analyze the Random Pursuit algorithm, which iteratively computes an approximate solution to the optimization problem by repeated optimization over a…
We propose a method for analyzing the distributed random coordinate descent algorithm for solving separable resource allocation problems in the context of an open multiagent system, where agents can be replaced during the process. In…
We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…
This paper first proposes an N-block PCPM algorithm to solve N-block convex optimization problems with both linear and nonlinear constraints, with global convergence established. A linear convergence rate under the strong second-order…