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We develop and analyze algorithms for distributionally robust optimization (DRO) of convex losses. In particular, we consider group-structured and bounded $f$-divergence uncertainty sets. Our approach relies on an accelerated method that…
This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
Recently, accelerated algorithms using the anchoring mechanism for minimax optimization and fixed-point problems have been proposed, and matching complexity lower bounds establish their optimality. In this work, we present the surprising…
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…
We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…
We introduce a new class of extremum seeking controllers able to achieve fixed time convergence to the solution of optimization problems defined by static and dynamical systems. Unlike existing approaches in the literature, the convergence…
Distributionally robust optimization (DRO) can improve the robustness and fairness of learning methods. In this paper, we devise stochastic algorithms for a class of DRO problems including group DRO, subpopulation fairness, and empirical…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Optimization theory has been widely studied in academia and finds a large variety of applications in industry. The different optimization models in their discrete and/or continuous settings have catered to a rich source of research…
This paper proposes a novel distributed optimization framework that addresses time-varying optimization problems without requiring explicit derivative information of the objective functions. Traditional distributed methods often rely on…
Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for…
In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…
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.…
We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…
In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being distributed over $n$ agents having access only to zeroth-order (ZO) information of the cost. This problem has various machine…
This paper is devoted to the study of acceleration methods for an inequality constrained convex optimization problem by using Lyapunov functions. We first approximate such a problem as an unconstrained optimization problem by employing the…
Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality,…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to…