相关论文: Factorization of Saddle-point Matrices in Dynamica…
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…
This paper presents a simple primal dual method named DPD which is a flexible framework for a class of saddle point problem with or without strongly convex component. The presented method has linearized version named LDPD and exact version…
This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…
This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal…
Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase…
This paper aims to address distributed optimization problems over directed and time-varying networks, where the global objective function consists of a sum of locally accessible convex objective functions subject to a feasible set…
Factorization of polynomials arises in numerous areas in symbolic computation. It is an important capability in many symbolic and algebraic computation. There are two type of factorization of polynomials. One is convention polynomial…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable $X$. This algorithm rests on the factorization $X=Y Y^T$, where the number of columns of Y fixes the rank of…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
Saddle-point problems have recently gained increased attention from the machine learning community, mainly due to applications in training Generative Adversarial Networks using stochastic gradients. At the same time, in some applications…
Addressing the interpretability problem of NMF on Boolean data, Boolean Matrix Factorization (BMF) uses Boolean algebra to decompose the input into low-rank Boolean factor matrices. These matrices are highly interpretable and very useful in…
Decentralized optimization methods have been in the focus of optimization community due to their scalability, increasing popularity of parallel algorithms and many applications. In this work, we study saddle point problems of sum type,…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…
Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques,…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct…
Despite the outstanding performance of deep neural networks in different applications, they are still computationally extensive and require a great number of memories. This motivates more research on reducing the resources required for…
In binary polynomial optimization, the goal is to find a binary point maximizing a given polynomial function. In this paper, we propose a novel way of formulating this general optimization problem, which we call factorized binary polynomial…