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In this paper, we develop a novel distributed algorithm for addressing convex optimization with both nonlinear inequality and linear equality constraints, where the objective function can be a general nonsmooth convex function and all the…
We study the distributed stochastic compositional optimization problems over directed communication networks in which agents privately own a stochastic compositional objective function and collaborate to minimize the sum of all objective…
We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the…
We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…
Projected Gradient Descent denotes a class of iterative methods for solving optimization programs. Its applicability to convex optimization programs has gained significant popularity for its intuitive implementation that involves only…
This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…
In this paper, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents' cost functions while obeying the network…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for…
In this paper we consider distributed optimization problems in which the cost function is separable (i.e., a sum of possibly non-smooth functions all sharing a common variable) and can be split into a strongly convex term and a convex one.…
This work is devoted to solving the composite optimization problem with the mixture oracle: for the smooth part of the problem, we have access to the gradient, and for the non-smooth part, only the one-point zero-order oracle is available.…
Zero-order (ZO) optimization is a powerful tool for dealing with realistic constraints. On the other hand, the gradient-tracking (GT) technique proved to be an efficient method for distributed optimization aiming to achieve consensus.…
Distributed optimization has a rich history. It has demonstrated its effectiveness in many machine learning applications, etc. In this paper we study a subclass of distributed optimization, namely decentralized optimization in a non-smooth…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…