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Motivated by applications to distributed optimization over networks and large-scale data processing in machine learning, we analyze the deterministic incremental aggregated gradient method for minimizing a finite sum of smooth functions…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
The alternating direction method of multipliers (ADMM) has been popular for solving many signal processing problems, convex or nonconvex. In this paper, we study an asynchronous implementation of the ADMM for solving a nonconvex nonsmooth…
In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing…
Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of…
In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…
We consider the problem of minimizing a sum of non-convex functions over a compact domain, subject to linear inequality and equality constraints. Approximate solutions can be found by solving a convexified version of the problem, in which…
This paper delves into the investigation of a distributed aggregative optimization problem within a network. In this scenario, each agent possesses its own local cost function, which relies not only on the local state variable but also on…
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…
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…
We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure. This algorithm uses sub-sampled derivatives…
Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…
We address the minimization of a smooth objective function under an $\ell_0$-constraint and simple convex constraints. When the problem has no constraints except the $\ell_0$-constraint, some efficient algorithms are available; for example,…
We propose a general scheme for solving convex and non-convex optimization problems on manifolds. The central idea is that, by adding a multiple of the squared retraction distance to the objective function in question, we "convexify" the…
Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…
We study distributed stochastic nonconvex optimization in multi-agent networks. We introduce a novel algorithmic framework for the distributed minimization of the sum of the expected value of a smooth (possibly nonconvex) function (the…
This paper considers a networked system with a finite number of users and supposes that each user tries to minimize its own private objective function over its own private constraint set. It is assumed that each user's constraint set can be…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…