Related papers: Computer-Assisted Search for Differential Equation…

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…

The dynamic slope scaling procedure is an approximation method successfully which solves the fixed charge network flow (FCNF) problem by iteratively linearizing the fixed cost. The parameterized dynamic slope scaling procedure adds an…

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited…

Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…

We propose a learning-based method for Lyapunov stability analysis of piecewise affine dynamical systems in feedback with piecewise affine neural network controllers. The proposed method consists of an iterative interaction between a…

In a Hilbert setting, we develop fast methods for convex unconstrained optimization. We rely on the asymptotic behavior of an inertial system combining geometric damping with temporal scaling. The convex function to minimize enters the…

We study the connections between ordinary differential equations and optimization algorithms in a non-Euclidean setting. We propose a novel accelerated algorithm for minimising convex functions over a convex constrained set. This algorithm…

We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…

It was shown recently by Su et al. (2016) that Nesterov's accelerated gradient method for minimizing a smooth convex function $f$ can be thought of as the time discretization of a second-order ODE, and that $f(x(t))$ converges to its…

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…

Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…

The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias component and study the extent to which SGD can match the…

Stochastic variance-reduced algorithms such as Stochastic Average Gradient (SAG) and SAGA, and their deterministic counterparts like the Incremental Aggregated Gradient (IAG) method, have been extensively studied in large-scale machine…

Deep Symbolic Optimization (DSO) is a novel computational framework that enables symbolic optimization for scientific discovery, particularly in applications involving the search for intricate symbolic structures. One notable example is…

The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…

From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we…

In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is…

Lion (Evolved Sign Momentum), a new optimizer discovered through program search, has shown promising results in training large AI models. It performs comparably or favorably to AdamW but with greater memory efficiency. As we can expect from…

Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature.…

A prototype tool to assist architects during the early design stage of floor plans has been developed, consisting of an Evolutionary Program for the Space Allocation Problem (EPSAP), which generates sets of floor plan alternatives according…