相关论文: Parallelizing the Circumcentered-Reflection Method

We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…

This paper introduces a parallel and distributed extension to the alternating direction method of multipliers (ADMM) for solving convex problem: minimize $\sum_{i=1}^N f_i(x_i)$ subject to $\sum_{i=1}^N A_i x_i=c, x_i\in \mathcal{X}_i$. The…

This paper presents an efficient parallel approximation scheme for a new class of min-max problems. The algorithm is derived from the matrix multiplicative weights update method and can be used to find near-optimal strategies for…

We propose the algorithm that solves the symmetric cone programs (SCPs) by iteratively calling the projection and rescaling methods the algorithms for solving exceptional cases of SCP. Although our algorithm can solve SCPs by itself, we…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Diffusion models excel at creating visually-convincing images, but they often struggle to meet subtle constraints inherent in the training data. Such constraints could be physics-based (e.g., satisfying a PDE), geometric (e.g., respecting…

In this work, the fast-convolving reproducing kernel particle method (FC-RKPM) is introduced. This method is hundreds to millions of times faster than the traditional RKPM for 3D meshfree simulations. In this approach, the meshfree…

Typical Structure-from-Motion (SfM) pipelines rely on finding correspondences across images, recovering the projective structure of the observed scene and upgrading it to a metric frame using camera self-calibration constraints. Solving…

We study the convergence rate of the alternating projection method (APM) applied to the intersection of an affine subspace and the second-order cone. We show that when they intersect non-transversally, the convergence rate is $O(k^{-1/2})$,…

We present successive convexification, a real-time-capable solution method for nonconvex trajectory optimization, with continuous-time constraint satisfaction and guaranteed convergence, that only requires first-order information. The…

Reward Models (RMs) are critical components in the Reinforcement Learning from Human Feedback (RLHF) pipeline, directly determining the alignment quality of Large Language Models (LLMs). Recently, Generative Reward Models (GRMs) have…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex…

We consider the problem of minimizing block-separable convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both…

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR data acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse…

Minimax optimization has become a central tool in machine learning with applications in robust optimization, reinforcement learning, GANs, etc. These applications are often nonconvex-nonconcave, but the existing theory is unable to identify…

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…

Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…

Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…