相关论文: Primal-dual splitting scheme with backtracking for…
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…
We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…
Image inverse problems have numerous applications, including image processing, super-resolution, and computer vision, which are important areas in image science. These application models can be seen as a three-function composite…
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use…
A novel approach for selecting appropriate reconstructions is implemented to the hyperbolic conservation laws in the high-order local polynomial-based framework, e.g., the discontinuous Galerkin (DG) and flux reconstruction (FR) schemes.…
An explicit first-order drift-randomized Milstein scheme for a regime switching stochastic differential equation is proposed and its bi-stability and rate of strong convergence are investigated for a non-differentiable drift coefficient.…
In this work, we propose a deep neural network architecture motivated by primal-dual splitting methods from convex optimization. We show theoretically that there exists a close relation between the derived architecture and residual…
This paper proposes and analyzes a tuning-free variant of Primal-Dual Hybrid Gradient (PDHG), and investigates its effectiveness for solving large-scale semidefinite programming (SDP). The core idea is based on the combination of two…
In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…
In this paper, we propose a model-based machine-learning approach for dual-polarization systems by parameterizing the split-step Fourier method for the Manakov-PMD equation. The resulting method combines hardware-friendly time-domain…
We propose a scalable preconditioned primal-dual hybrid gradient algorithm for solving partial differential equations (PDEs). We multiply the PDE with a dual test function to obtain an inf-sup problem whose loss functional involves…
In the FDR-controlling literature, mirror statistics offer a flexible alternative to $p$-value based procedures. When prior information is available, however, it is unclear how to incorporate mirror statistics in a principled way, and the…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Distance weighted discrimination (DWD) was originally proposed to handle the data piling issue in the support vector machine. In this paper, we consider the sparse penalized DWD for high-dimensional classification. The state-of-the-art…
In this paper we propose a class of randomized primal-dual methods to contend with large-scale saddle point problems defined by a convex-concave function $\mathcal{L}(\mathbf{x},y)\triangleq\sum_{i=1}^m f_i(x_i)+\Phi(\mathbf{x},y)-h(y)$. We…
Binarization of digital documents is the task of classifying each pixel in an image of the document as belonging to the background (parchment/paper) or foreground (text/ink). Historical documents are often subjected to degradations, that…
We study a discrete-time approximation for solutions of systems of decoupled forward-backward doubly stochastic differential equations (FBDSDEs). Assuming that the coefficients are Lipschitz-continuous, we prove the convergence of the…
In this work, we investigate the application of deep learning methods for computed tomography in the context of having a low-data regime. As motivation, we review some of the existing approaches and obtain quantitative results after…
Balancing domain decomposition by constraints (BDDC) algorithms with adaptive primal constraints are developed in a concise variational framework for the weighted plane wave least-squares (PWLS) discritization of Helmholtz equations with…
We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower…