Regula falsi based automatic regularization method for PDE constrained optimization

Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems

In this article, we motivate, derive and test effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems, which arise in PDE constrained optimization problems. We consider the distributed control problem involving the heat equation with two different functionals, and the Neumann boundary control problem involving Poisson’s equation and the heat e...

Algorithms for PDE-Constrained Optimization

In this paper we review a number of algorithmic approaches for solving optimization problems with PDE constraints. Most of these methods were originally developed for finite dimensional problems. When applied to optimization problems with PDE constraints, new aspects become important. For instance, (discretized) PDE-constrained problems are inherently large-scale. Some aspects, like mesh indepe...

Multigrid One-Shot Method for PDE-Constrained Optimization Problems

This paper presents a numerical method for PDE-constrained optimization problems. These problems arise in many fields of science and engineering including those dealing with real applications. The physical problem is modeled by partial differential equations (PDEs) and involve optimization of some quantity. The PDEs are in most cases nonlinear and solved using numerical methods. Since such nume...

Inexact Interior-Point Method for PDE-Constrained Nonlinear Optimization

Adjoint method for a tumor growth PDE-constrained optimization problem

In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists on a coupled system of partial differential equations whose spatial domain is the tum...