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The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

This note is devoted to the distributed optimization problem of multi-agent systems with nonconvex velocity constraints, nonuniform position constraints and nonuniform stepsizes. Two distributed constrained algorithms with nonconvex…

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…

Distributed optimization finds applications in large-scale machine learning, data processing and classification over multi-agent networks. In real-world scenarios, the communication network of agents may encounter latency that may affect…

In this work, we study a novel class of projection-based algorithms for linearly constrained problems (LCPs) which have a lot of applications in statistics, optimization, and machine learning. Conventional primal gradient-based methods for…

In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…

Establishing a fast rate of convergence for optimization methods is crucial to their applicability in practice. With the increasing popularity of deep learning over the past decade, stochastic gradient descent and its adaptive variants…

In this work, multiplicative stochasticity is applied to the learning rate of stochastic optimization algorithms, giving rise to stochastic learning-rate schemes. In-expectation theoretical convergence results of Stochastic Gradient Descent…

Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…

This paper considers the efficient minimization of the infinite time average of a stationary ergodic process in the space of a handful of design parameters which affect it. Problems of this class, derived from physical or numerical…

Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…

This paper proposes an accelerated consensus-based distributed iterative algorithm for resource allocation and scheduling. The proposed gradient-tracking algorithm introduces an auxiliary variable to add momentum towards the optimal state.…

This paper considers a problem where multiple users make repeated decisions based on their own observed events. The events and decisions at each time step determine the values of a utility function and a collection of penalty functions. The…

In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is not necessarily convex. A global stochastic maximum principle is…

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized…

In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…

This paper investigates the problem of tracking solutions of stochastic optimization problems with time-varying costs that depend on random variables with decision-dependent distributions. In this context, we propose the use of an online…

We study a distributed framework for stochastic optimization which is inspired by models of collective motion found in nature (e.g., swarming) with mild communication requirements. Specifically, we analyze a scheme in which each one of $N >…

We introduce the Projected Push-Pull algorithm that enables multiple agents to solve a distributed constrained optimization problem with private cost functions and global constraints, in a collaborative manner. Our algorithm employs…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…