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A variationally consistent generalized variable formulation of the elastoplastic rate problem

Claudia Comi, Umberto Perego (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The elastoplastic rate problem is formulated as an unconstrained saddle point problem which, in turn, is obtained by the Lagrange multiplier method from a kinematic minimum principle. The finite element discretization and the enforcement of the min-max conditions for the Lagrangean function lead to a set of algebraic governing relations (equilibrium, compatibility and constitutive law). It is shown how important properties of the continuum problem (like, e.g., symmetry, convexity, normality) carry...

About the relation between some optimality conditions

Jan Palata (1984)

Aplikace matematiky

The relation between the general optimality conditions in terms of contact cones and the Kuhn-Tucker conditions in the special case of pseudo-convex and quasi-convex functions and their consequence to Lagrangian multipliers are given.

Adaptive finite element method for shape optimization

Pedro Morin, Ricardo H. Nochetto, Miguel S. Pauletti, Marco Verani (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution...

Adaptive mesh refinement strategy for a non conservative transport problem

Benjamin Aymard, Frédérique Clément, Marie Postel (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Long time simulations of transport equations raise computational challenges since they require both a large domain of calculation and sufficient accuracy. It is therefore advantageous, in terms of computational costs, to use a time varying adaptive mesh, with small cells in the region of interest and coarser cells where the solution is smooth. Biological models involving cell dynamics fall for instance within this framework and are often non conservative to account for cell division. In that case...

All-at-once preconditioning in PDE-constrained optimization

Tyrone Rees, Martin Stoll, Andy Wathen (2010)

Kybernetika

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...

An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Kieweg, Yuri Iliash, Ronald H. W. Hoppe, Michael Hintermüller (2008)

ESAIM: Control, Optimisation and Calculus of Variations

We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...

An a posteriori error analysis of adaptive finite element methods for distributed elliptic control problems with control constraints

Michael Hintermüller, Ronald H.W. Hoppe, Yuri Iliash, Michael Kieweg (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We present an a posteriori error analysis of adaptive finite element approximations of distributed control problems for second order elliptic boundary value problems under bound constraints on the control. The error analysis is based on a residual-type a posteriori error estimator that consists of edge and element residuals. Since we do not assume any regularity of the data of the problem, the error analysis further invokes data oscillations. We prove reliability and efficiency of the error estimator...

An active set strategy based on the augmented Lagrangian formulation for image restoration

Kazufumi Ito, Karl Kunisch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by...

An algorithm for construction of ε-value functions for the Bolza control problem

Edyta Jacewicz (2001)

International Journal of Applied Mathematics and Computer Science

The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper...

An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel

Gupta Nupur, Nataraj Neela (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...

An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel

Gupta Nupur, Nataraj Neela (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...

Currently displaying 61 – 80 of 517