A Douglas–Rachford method for sparse extreme learning machine

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from ex…

A GPU-accelerated augmented Lagrangian based L1-mean curvature Image denoising algorithm implementation

This paper presents a graphics processing unit (GPU) implementation of a recently published augmented Lagrangian based L1-mean curvature image denoising algorithm. The algorithm uses a particular alternating direction method of multipliers to reduce the related saddle-point problem to an iterative sequence of four simpler minimization problems. Two of these subproblems do not contain the derivatives of the unknown variables and can therefore be solved point-wise without inter-process communication. Inparticular, this facilitates the efficient solution of the subproblem that deals with the non-convex term in the original objective function by modern GPUs. The two remaining subproblems are so…

A Domain Decomposition/Nash Equilibrium Methodology for the Solution of Direct and Inverse Problems in Fluid Dynamics with Evolutionary Algorithms