Showing papers by "Fredi Tröltzsch published in 1999"

On the Lagrange--Newton--SQP Method for the Optimal Control of Semilinear Parabolic Equations

Abstract: A class of Lagrange--Newton--SQP methods is investigated for optimal control problems governed by semilinear parabolic initial-boundary value problems. Distributed and boundary controls are given, restricted by pointwise upper and lower bounds. The convergence of the method is discussed in appropriate Banach spaces. Based on a weak second order sufficient optimality condition for the reference solution, local quadratic convergence is proved. The proof is based on the theory of Newton methods for generalized equations in Banach spaces.

Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations

Abstract: In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem.

Optimal control of semilinear parabolic equations with state-constraints of bottleneck type

Abstract: We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear programming problems.

Optimal Control of Partial Differential Equations : International Conference in Chemnitz, Germany, April 20-25, 1998

Abstract: Well-posedness of semilinear heat equations with iterated logarithms, Paolo Albano et al uniform stability of nonlinear thermoelastic plates with free boundary conditions, George Avalos et al exponential bases in Sobolev spaces in control and observation problems, Sergei A. Avdonin et al sampling and interpolation of functions with multi-band spectra and controllability problems, Sergei Avdonin, William Moran discretization of the controllability Grammian in view of exact boundary control - the case of thin plates, Frederic Bourquin et al stability of holomorphic semigroup systems under nonlinear boundary perturbations, Francesca Bucci shape control in hyperbolic problems, John Cagnol, Jean-Paul Zolesia second order optimality conditions for some control problems of semilinear elliptic equations with integral state constraints, Eduardo Casas intrinsic P(2,1) thin shell models and Naghdi's models without A priori assumption on the stress tensor, Michel C. Delfour on the approximate controllability for some explosive parabolic problems, J.I. Diaz, J.L. Lions Frechet-differentiability and sufficient optimality conditions for shape functional, Karsten Eppler state constrained optimal control for some quasilinear parabolic equations, Luis A. Fernandez controllability property for the Navier-Stokes equations, Andrei V. Fursikov shape sensitivity and large deformation of the domain for Norton-Hoff flows, Nicolas Gomez, Jean-Paul Zolesio on a distributed control law with an application to the control of unsteady flow around a cylinder, Michael Hinze, Andreas Kauffmann homogenization of a model describing vibration of nonlinear thin plates excited by piezopatches, K.-H. Hoffmann, N.D. Botkin stabilization of the dynamic system of elasticity by nonlinear boundary feedback, Mary Ann Horn Griffith formula and Rice-Cherepanov's integral for elliptic equations with unilateral conditions in nonsmooth domains, A.M. Khludnev, J. Sokolowski a domain optimization problem for a nonlinear thermoelastic system, A. Myslinski, F. Troltzch approximate controllability for a hydro-elastic model in a rectangular domain, Axel Osses, Jean-Pierre Puel noncooperative games with elliptic systems, Tomas Roubicek incomplete indefinite decompositions as multigrid smoothers for KKT systems, Volker H. Schulz domain optimization for the Navier-Stokes equations by an embedding domain method, Thomas Slawig on the approximation and optimization of fourth order elliptic systems, J. Sprekels, D. Tiba. (Part contents).

Second Order Optimality Conditions for Some Control Problems of Semilinear Elliptic Equations with Integral State Constraints

Abstract: In this paper we discuss necessary and sufficient second order optimality conditions for control problems of semilinear elliptic equations with pointwise control constraints as well as integral state constraints. We consider the case of a boundary control problem, the state equation being described by a Neumann problem. The presence of state constraints along with pointwise control constraints causes some known difficulties in the proof of optimality conditions. Due to the specific integral form of the state-constraints, here we are able to considerably tighten the gap between second order necessary and sufficient condition. The analysis is based on some constraint qualification.

A Domain Optimization Problem for a Nonlinear Thermoelastic System

Abstract: A shape optimization problem for a thermoelastic system with a nonlinear boundary condition is considered. Using the material derivative method as well as the results of regularity of solutions to the state system, the sensitivity analysis of the solution to this system with respect to the variation of the domain is performed and necessary optimality conditions are derived.