Search results for "augmented Lagrangian method"

Optimality Conditions for Non-Qualified Parabolic Control Problems

1994

We consider parabolic state constrained optimal control problems where the usual Slater condition is not necessarily satisfied. Instead, a weaker interiority property is assumed. Optimality conditions with a Lagrange multiplier are given. As an application we present an augmented Lagrangian algorithm. Numerical test results are included.

Solution of the Skyrme-Hartree–Fock–Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): A new version of …

2017

We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb ene…

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

2015

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…

Gradient-enhanced model and its micromorphic regularization for simulation of Lüders-like bands in shape memory alloys

2018

Abstract Shape memory alloys, notably NiTi, often exhibit softening pseudoelastic response that results in formation and propagation of Luders-like bands upon loading, for instance, in uniaxial tension. A common approach to modelling softening and strain localization is to resort to gradient-enhanced formulations that are capable of restoring well-posedness of the boundary-value problem. This approach is also followed in the present paper by introducing a gradient-enhancement into a simple one-dimensional model of pseudoelasticity. In order to facilitate computational treatment, a micromorphic-type regularization of the gradient-enhanced model is subsequently performed. The formulation empl…

HHT-α and TR-BDF2 schemes for dynamic contact problems

2023

This work focuses on the numerical performance of HHT-α and TR-BDF2 schemes for dynamic frictionless unilateral contact problems between an elastic body and a rigid obstacle. Nitsche's method, the penalty method, and the augmented Lagrangian method are considered to handle unilateral contact conditions. Analysis of the convergence of an opposed value of the parameter α for the HHT-α method is achieved. The mass redistribution method has also been tested and compared with the standard mass matrix. Numerical results for 1D and 3D benchmarks show the functionality of the combinations of schemes and methods used.

An Automatic Differentiation Based Approach to the Level Set Method

2015

This paper discusses an implementation of the parametric level set method. Adjoint approach is used to perform the sensitivity analysis, but contrary to standard implementations, the state problem is differentiated in its discretized form. The required partial derivatives are computed using tools of automatic differentiation, which avoids the need to derive the adjoint problem from the governing partial differential equation. The augmented Lagrangian approach is used to enforce volume constraints, and a gradient based optimization method is used to solve the subproblems. Applicability of the method is demonstrated by repeating well known compliance minimization studies of a cantilever beam …

Statistical Modeling for the Flow of Short Fibers Composites

1994

Numerical results are given for the flow of fiber composites modelled as suspensions of non spherical particles. In this framework, because the many particles rotate, their state of orientation is described with a statistical approach. We used these methods to compute coupled solutions in which the orientation of the particles is affected by the flow and the flow itself depends on the orientation of the particles. The computation methods involve an augmented lagrangian approach and a streamline upwind petrov galerkin formulation to solve the convective orientation equation.

On GPU-accelerated fast direct solvers and their applications in image denoising

2015

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

2015

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…