A SQP-Semismooth Newton-type Algorithm applied to Control of the instationary Navier--Stokes System Subject to Control Constraints

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...

Optimization Methods in Banach Spaces

In this chapter we present a selection of important algorithms for optimization problems with partial differential equations. The development and analysis of these methods is carried out in a Banach space setting. We begin by introducing a general framework for achieving global convergence. Then, several variants of generalized Newton methods are derived and analyzed. In particular, necessary a...

Optimal and instantaneous control of the instationary Navier-Stokes equations

Contents Danksagung 1 Chapter 1. Introduction 5 1. Aims and scope of flow control 5 2. A brief review in active flow control 8 Chapter 2. Notation and preliminary results 15 1. Quasi-Stokes problems 15 2. Instationary Navier-Stokes equations in 2d 16 3. Navier-Stokes numerics 19 Chapter 3. Optimal control of the instationary Navier-Stokes equations 23 1. The optimal control problem 23 2. Deriva...

The SQP-method for tracking type control of the instationary Navier-Stokes equations

Numerical Solution of Optimal Control Problems with Convex Control Constraints

We study optimal control problems with vector-valued controls. As model problem serves the optimal distributed control of the instationary Navier-Stokes equations. In the article, we propose a solution strategy to solve optimal control problems with pointwise convex control constraints. It involves a SQP-like step with an imbedded active-set algorithm. The efficiency of that method is demonstra...