相关论文: The Geometry of Constrained Optimization: Constrai…

We present a self-supervised approach to estimate flow in camera image and top-view grid map sequences using fully convolutional neural networks in the domain of automated driving. We extend existing approaches for self-supervised optical…

We develop a fast and scalable numerical approach to solve Wasserstein gradient flows (WGFs), particularly suitable for high-dimensional cases. Our approach is to use general reduced-order models, like deep neural networks, to parameterize…

Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization…

This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair…

This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…

We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

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…

Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite its ubiquity, the mechanism underlying this behavior remains…

We present a general framework of designing efficient dynamic approximate algorithms for optimization on undirected graphs. In particular, we develop a technique that, given any problem that admits a certain notion of vertex sparsifiers,…

In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…

Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for…

The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…

Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…

This paper considers a nonconvex optimization problem that evolves over time, and addresses the synthesis and analysis of regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized…

Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…

Gradient regularization (GR) is a method that penalizes the gradient norm of the training loss during training. While some studies have reported that GR can improve generalization performance, little attention has been paid to it from the…

We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics, both in time and space, which include the relaxation schemes by S. Jin and Z. Xin. These methods can use CFL number larger…

We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…

This paper studies the robust isolated calmness property of the KKT solution mapping of a class of nonsmooth optimization problems on Riemannian manifolds. The manifold versions of the Robinson constraint qualification, the strict Robinson…