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Large-scale constrained optimization is pivotal in modern scientific, engineering, and industrial computation, often involving complex systems with numerous variables and constraints. This paper provides a unified and comprehensive…
We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the…
The advancement of sensing technology has driven the widespread application of high-dimensional data. However, issues such as missing entries during acquisition and transmission negatively impact the accuracy of subsequent tasks. Tensor…
This paper is concerned with estimating unknown multi-dimensional frequencies from linear compressive measurements. This is accomplished by employing the recently proposed atomic norm minimization framework to recover these frequencies…
In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…
The matrix low-rank approximation problem with additional convex constraints can find many applications and has been extensively studied before. However, this problem is shown to be nonconvex and NP-hard; most of the existing solutions are…
Deep learning-based image compression algorithms typically focus on designing encoding and decoding networks and improving the accuracy of entropy model estimation to enhance the rate-distortion (RD) performance. However, few algorithms…
Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…
Recent techniques such as retrieval-augmented generation or chain-of-thought reasoning have led to longer contexts and increased inference costs. Context compression techniques can reduce these costs, but the most effective approaches…
The Alternating Direction Method of Multipliers (ADMM) is widely used for linearly constrained convex problems. It is proven to have an $o(1/\sqrt{K})$ nonergodic convergence rate and a faster $O(1/K)$ ergodic rate after ergodic averaging,…
Herein, security of deep neural network against adversarial attack is considered. Existing compressive sensing based defence schemes assume that adversarial perturbations are usually on high frequency components, whereas recently it has…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
The ability of widely distributed radar systems to capture diverse spatial scattering properties substantially improves radar imaging performance. Traditional imaging methods leverage regularized optimization techniques to reconstruct…
Accurately establishing the state of large-scale quantum systems is an important tool in quantum information science; however, the large number of unknown parameters hinders the rapid characterisation of such states, and reconstruction…
This paper focuses on the decentralized optimization problem, where agents in a network cooperate to minimize the sum of their local objective functions by information exchange and local computation. Based on the alternating direction…
The memory challenges associated with training Large Language Models (LLMs) have become a critical concern, particularly when using the Adam optimizer. To address this issue, numerous memory-efficient techniques have been proposed, with…
This work develops a novel set of algorithms, alternating Gradient Descent (GD) and minimization for MRI (altGDmin-MRI1 and altGDmin-MRI2), for accelerated dynamic MRI by assuming an approximate low-rank (LR) model on the matrix formed by…
This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with…
L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In…
Hyperbolic deep learning has become a growing research direction in computer vision due to the unique properties afforded by the alternate embedding space. The negative curvature and exponentially growing distance metric provide a natural…