Related papers: Restricted Linearized Augmented Lagrangian Method …
Statistical image reconstruction (SIR) methods are studied extensively for X-ray computed tomography (CT) due to the potential of acquiring CT scans with reduced X-ray dose while maintaining image quality. However, the longer reconstruction…
In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with…
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…
There are two main strategies for improving the projection-based reduced order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM bases that…
Image segmentation is a fundamental topic in image processing and has been studied for many decades. Deep learning-based supervised segmentation models have achieved state-of-the-art performance but most of them are limited by using…
We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…
In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and some candidate image on a large collection of subboxes. The…
This paper is concerned with augmented Lagrangian methods for the treatment of fully convex composite optimization problems. We extend the classical relationship between augmented Lagrangian methods and the proximal point algorithm to the…
The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the…
We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture…
We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each…
The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original…
We develop a fast and robust algorithm for solving large scale convex composite optimization models with an emphasis on the $\ell_1$-regularized least squares regression (Lasso) problems. Despite the fact that there exist a large number of…
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…
The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
To construct a parallel approach for solving optimization problems with orthogonality constraints is usually regarded as an extremely difficult mission, due to the low scalability of the orthonormalization procedure. However, such demand is…