相关论文: Log-Averaged Mirror Prox for Fast, Large-Scale Opt…

We consider strongly-convex-strongly-concave saddle point problems assuming we have access to unbiased stochastic estimates of the gradients. We propose a stochastic accelerated primal-dual (SAPD) algorithm and show that SAPD sequence,…

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…

In this paper, we propose a continuous-time primal-dual approach for linearly constrained multiobjective optimization problems. A novel dynamical model, called accelerated multiobjective primal-dual flow, is presented with a second-order…

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…

This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…

We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex…

End-to-end autonomous driving systems powered by Vision-Language-Action (VLA) models achieve strong performance on common driving scenarios, yet remain brittle in rare but safety-critical long-tail situations such as active construction…

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…

To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…

We consider mixed model of traffic flow distribution in large networks (BMW model, 1954 & Stable Dynamic model, 1999). We build dual problem and consider primal-dual mirror descent method for the dual problem. There are two ways to recover…

Perspective distortion (PD) leads to substantial alterations in the shape, size, orientation, angles, and spatial relationships of visual elements in images. Accurately determining camera intrinsic and extrinsic parameters is challenging,…

This paper addresses the bilinearly coupled minimax optimization problem: $\min_{x \in \mathbb{R}^{d_x}}\max_{y \in \mathbb{R}^{d_y}} \ f_1(x) + f_2(x) + y^{\top} Bx - g_1(y) - g_2(y)$, where $f_1$ and $g_1$ are smooth convex functions,…

In this paper, we consider a proximal linearized alternating direction method of multipliers (PL-ADMM) for solving linearly constrained nonconvex and possibly nonsmooth optimization problems. The algorithm is generalized by using variable…

We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and…

We present implicit-explicit (IMEX) kinetic simulations of weakly collisional parallel plasma transport in magnetic mirror configurations using the continuum code \textsc{COGENT}. The numerical scheme employs a Jacobian-free Newton--Krylov…

We propose Mirror Descent Optimal Transport (MDOT), a novel method for solving discrete optimal transport (OT) problems with high precision, by unifying temperature annealing in entropic-regularized OT (EOT) with mirror descent techniques.…

First-order primal-dual methods are appealing for their low memory overhead, fast iterations, and effective parallelization. However, they are often slow at finding high accuracy solutions, which creates a barrier to their use in…

We provide improved convergence rates for constrained convex-concave min-max problems and monotone variational inequalities with higher-order smoothness. In min-max settings where the $p^{th}$-order derivatives are Lipschitz continuous, we…

Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…

Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. They are unsatisfactory in terms of…