Related papers: Splitting Method for Support Vector Machine in Rep…
This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…
Training structured prediction models is time-consuming. However, most existing approaches only use a single machine, thus, the advantage of computing power and the capacity for larger data sets of multiple machines have not been exploited.…
Although Support Vector Machine (SVM) algorithm has a high generalization property to classify for unseen examples after training phase and it has small loss value, the algorithm is not suitable for real-life classification and regression…
In this paper, we propose an algorithm combining the forward-backward splitting method and the alternative projection method for solving the system of splitting inclusion problem. We want to find a point in the interception of a finite…
A typical approach in estimating the learning rate of a regularized learning scheme is to bound the approximation error by the sum of the sampling error, the hypothesis error and the regularization error. Using a reproducing kernel space…
This paper studies the problem of Kronecker-structured sparse vector recovery from an underdetermined linear system with a Kronecker-structured dictionary. Such a problem arises in many real-world applications such as the sparse channel…
Compressed sensing (CS) techniques demand significant storage and computational resources, when recovering high-dimensional sparse signals. Block CS (BCS), a special class of CS, addresses both the storage and complexity issues by…
We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the…
Dual Coordinate Descent (DCD) and Block Dual Coordinate Descent (BDCD) are important iterative methods for solving convex optimization problems. In this work, we develop scalable DCD and BDCD methods for the kernel support vector machines…
We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…
We consider ill-posed linear operator equations with operators acting between Banach spaces. For solution approximation, the methods of choice here are projection methods onto finite dimensional subspaces, thus extending existing results…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…
The forward-backward splitting algorithm is a popular operator-splitting method for solving monotone inclusion of the sum of a maximal monotone operator and a cocoercive operator. In this paper, we present a new convergence analysis of a…
Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new…
In this paper, we present a fast and accurate numerical scheme for the solution of fifth-order boundary-value problems. We apply the reproducing kernel Hilbert space method (RKHSM) for solving this problem. The analytic results of the…
This paper presents a kernel-based discriminative learning framework on probability measures. Rather than relying on large collections of vectorial training examples, our framework learns using a collection of probability distributions that…
Let us consider a case where all of the elements in some continuous slices are missing in tensor data. In this case, the nuclear-norm and total variation regularization methods usually fail to recover the missing elements. The key problem…
The alternating direction method of multipliers (ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving a two-block separable…
We study the extragradient method for solving vector quasi-equilibrium problems in Banach spaces, which generalizes the extragradient method for vector equilibrium problems and scalar quasi-equilibrium problems. We propose a regularization…