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In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in…
Phase retrieval can be expressed as one non-convex constrained optimization problem to identify one phase minimizer in the primal space. Many iterative transform techniques have been proposed to identify the minimizer, e.g., relaxed…
Optimal transport on a graph focuses on finding the most efficient way to transfer resources from one distribution to another while considering the graph's structure. This paper introduces a new distributed algorithm that solves the optimal…
Douglas-Rachford splitting and its equivalent dual formulation ADMM are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on…
We propose a boundary neuron method with random features (BNM-RF) for solving partial differential equations. The method approximates the unknown boundary function by a shallow network within the boundary integral formulation. With randomly…
The rate-distortion-perception (RDP) tradeoff characterizes the fundamental limits of lossy compression by jointly considering bitrate, reconstruction fidelity, and perceptual quality. While recent neural compression methods have improved…
The Alternating Minimization Algorithm (AMA) has been proposed by Tseng to solve convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be…
This paper develops a scalable new algorithm, called NysADMM, to minimize a smooth convex loss function with a convex regularizer. NysADMM accelerates the inexact Alternating Direction Method of Multipliers (ADMM) by constructing a…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
RMSProp and ADAM continue to be extremely popular algorithms for training neural nets but their theoretical convergence properties have remained unclear. Further, recent work has seemed to suggest that these algorithms have worse…
Non-reference metrics (NRMs) can assess the visual quality of images and videos without a reference, making them well-suited for the evaluation of user-generated content. Nonetheless, rate-distortion optimization (RDO) in video coding is…
In this paper we consider the Nonnegative Matrix Factorization (NMF) problem: given an (elementwise) nonnegative matrix $V \in \R_+^{m\times n}$ find, for assigned $k$, nonnegative matrices $W\in\R_+^{m\times k}$ and $H\in\R_+^{k\times n}$…
To deploy deep learning algorithms on resource-limited scenarios, an emerging device-resistive random access memory (ReRAM) has been regarded as promising via analog computing. However, the practicability of ReRAM is primarily limited due…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of action…
For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…
Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…
Despite significant progress in deep learning-based optical flow methods, accurately estimating large displacements and repetitive patterns remains a challenge. The limitations of local features and similarity search patterns used in these…
This paper presents optimal scaling of the alternating directions method of multipliers (ADMM) algorithm for a class of distributed quadratic programming problems. The scaling corresponds to the ADMM step-size and relaxation parameter, as…
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…