Related papers: Fixed Point Algorithm Based on Quasi-Newton Method…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Quasi-Newton methods refer to a class of algorithms at the interface between first and second order methods. They aim to progress as substantially as second order methods per iteration, while maintaining the computational complexity of…
We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…
In this paper, we devise a $\operatorname{prox}$-based semi-smooth Newton method for the non-differentiable TV-minimization problem. To this end, the primal-dual optimality conditions are reformulated as a nonlinear operator equation with…
Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…
Designing efficient quasi-Newton methods is an important problem in nonlinear optimization and the solution of systems of nonlinear equations. From the perspective of the matrix approximation process, this paper presents a unified framework…
Total variation (TV) regularization is popular in image restoration and reconstruction due to its ability to preserve image edges. To date, most research activities on TV models concentrate on image restoration from blurry and noisy…
Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…
The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…
The paper proposes and justifies a new algorithm of the proximal Newton type to solve a broad class of nonsmooth composite convex optimization problems without strong convexity assumptions. Based on advanced notions and techniques of…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Non-uniform blind deblurring for general dynamic scenes is a challenging computer vision problem as blurs arise not only from multiple object motions but also from camera shake, scene depth variation. To remove these complicated motion…
Superlinear convergence has been an elusive goal for black-box nonsmooth optimization. Even in the convex case, the subgradient method is very slow, and while some cutting plane algorithms, including traditional bundle methods, are popular…
In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…
We present a new method for blind motion deblurring that uses a neural network trained to compute estimates of sharp image patches from observations that are blurred by an unknown motion kernel. Instead of regressing directly to patch…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
Image deconvolution is still to be a challenging ill-posed problem for recovering a clear image from a given blurry image, when the point spread function is known. Although competitive deconvolution methods are numerically impressive and…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition…
We consider sequential and parallel decomposition methods for a dual problem of a general total variation minimization problem with applications in several image processing tasks, like image inpainting, estimation of optical flow and…