Related papers: Nonnegative Tensor Decomposition Via Collaborative…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that complexity by…
A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current…
We consider the problem of structured canonical polyadic decomposition. If the size of the problem is very big, then stochastic gradient approaches are viable alternatives to classical methods, such as Alternating Optimization and…
The solution of nonsymmetric but positive definite (NSPD) systems arising from advection-diffusion problems is an important research topic in science and engineering. Balancing domain decomposition by constraints with an adaptive coarse…
A novel canonical duality theory (CDT) is presented for solving general bilevel mixed integer nonlinear optimization governed by linear and quadratic knapsack problems. It shows that the challenging knapsack problems can be solved…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…
Given a set of image denoisers, each having a different denoising capability, is there a provably optimal way of combining these denoisers to produce an overall better result? An answer to this question is fundamental to designing an…
This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…
Photonic neuromorphic computing offers a promising route to overcoming the limitations of conventional von Neumann architectures by exploiting the high bandwidth, low latency, and massive parallelism of optical systems. However, most…
We address the unsupervised learning of several interconnected problems in low-level vision: single view depth prediction, camera motion estimation, optical flow, and segmentation of a video into the static scene and moving regions. Our key…
Continual learning (CL) breaks off the one-way training manner and enables a model to adapt to new data, semantics and tasks continuously. However, current CL methods mainly focus on single tasks. Besides, CL models are plagued by…
Copositive optimization is a special case of convex conic programming, and it consists of optimizing a linear function over the cone of all completely positive matrices under linear constraints. Copositive optimization provides powerful…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns…
In recent years, convolutional neural networks (CNNs) have become deeper in order to achieve better classification accuracy in image classification. However, it is difficult to deploy the state-of-the-art deep CNNs for industrial use due to…
Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…
The decomposition of non-stationary signals is an important and challenging task in the field of signal time-frequency analysis. In the recent two decades, many signal decomposition methods led by the empirical mode decomposition, which was…
Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…