Related papers: A Hardware Accelerator for the Goemans-Williamson …

The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…

Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…

In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski and the recent…

Most commercially available fixed-wing aerial vehicles (FWV) can carry only small, lightweight computing hardware such as Jetson TX2 onboard. Solving non-linear trajectory optimization on these computing resources is computationally…

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

Quantum optimization algorithms, such as the Quantum Approximate Optimization Algorithm, are emerging as promising heuristics for solving complex combinatorial problems. To improve performance, several extensions to the standard QAOA…

Black-box optimization is primarily important for many compute-intensive applications, including reinforcement learning (RL), robot control, etc. This paper presents a novel theoretical framework for black-box optimization, in which our…

This paper deals with the minimization of large sum of convex functions by Inexact Newton (IN) methods employing subsampled functions, gradients and Hessian approximations. The Conjugate Gradient method is used to compute the inexact Newton…

In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…

In this paper, we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian, we…

This paper proposes and justifies two globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are…

The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently…

Robust estimation is essential in computer vision, robotics, and navigation, aiming to minimize the impact of outlier measurements for improved accuracy. We present a fast algorithm for Geman-McClure robust estimation, FracGM, leveraging…

We propose a globally-accelerated, first-order method for the optimization of smooth and (strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We achieve the same convergence rates as Nesterov's accelerated…

This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…

We propose a scalable framework for solving the Maximum Cut (MaxCut) problem in large graphs using projected gradient ascent on quadratic objectives. Our approach is differentiable and leverages GPUs for gradient-based optimization. It is…

Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…

We describe how variable precision floating point arithmetic can be used in the iterative solver GMRES. We show how the precision of the inner products carried out in the algorithm can be reduced as the iterations proceed, without affecting…