Second Order Sufficient Conditions and Sequential Quadratic Programming
for Optimal Control Problems with Mixed Constraints
- Project Staff: Nataliya Metla
- Project Leader: Arnd Rösch
- Project Leader: Roland Griesse
Project Abstract
Many technical processes are described by partial differential equations. The optimization of such processes or identification of material parameters leads to optimal control problems for partial differential equations. Naturally, some quantities of the process have to be restricted to admissible ranges. The scope of this project covers optimal control of elliptic and parabolic partial differential equations with pointwise inequality constraints in space and time.Typically, nonlinear functions are involved in real-life problems. In turn, necessary and sufficient optimality conditions of nonlinear optimal control problems contain first and second derivatives of these nonlinearities. Sufficient optimality conditions can ensure stability under perturbations of the solutions of the investigated optimal control problems. Moreover, they represent the key to prove convergence of fast and efficient numerical methods.
Until now, sufficient optimality conditions, stability results, and convergence of fast numerical methods are only known in case the pointwise inequality constraints affect solely the controls of the system. In contrast, real-life problems contain typically both, pointwise inequality constraints for controls and process quantities, i.e., states. Inequality constraints for process quantities alone lead to mathematical problems which are far from being solved.
In this project, we will establish sufficient optimality conditions and we will prove stability results and convergence of the SQP-method for mixed constrained optimal control problems: Pointwise inequality conditions containing controls and process quantities are simultaneously involved in such constraints. These theory developed in this project will guarantee reliable numerical results for arbitrary fine discretizations of the involved partial differential equations.
Keywords and AMS Classification
- optimal control
- convergence theory
- partial differential equations
- sufficient optimality conditions
- SQP method
- mixed constraints
- R. Griesse, N. Metla and A. Rösch
Local Quadratic Convergence of SQP for Elliptic Optimal Control Problems with Nonlinear Mixed Control-State Constraints
submitted, 2008 - R. Griesse, N. Metla and A. Rösch
Local Quadratic Convergence of SQP for Elliptic Optimal Control Problems with Mixed Control-State Constraints
submitted, 2007 - W. Alt, R. Griesse, N. Metla and A. Rösch
Lipschitz Stability for Elliptic Optimal Control Problems with Mixed Control-State Constraints
submitted, 2006 - R. Griesse
Lipschitz Stability of Solutions to Some State-Constrained Elliptic Optimal Control Problems
Journal of Analysis and its Applications (ZAA), 25, p.435-455, 2006 - A. Rösch and F. Tröltzsch
Existence of Regular Lagrange Multipliers for a Nonlinear Elliptic Optimal Control Problem with Pointwise Control-State Constraints
SIAM Journal on Control and Optimization (SICON), 45(2), p.548-564, 2006 - A. Rösch and F. Tröltzsch
Sufficient Second-Order Optimality Conditions for an Elliptic Optimal Control Problem with Pointwise Control-State Constraints
to appear in: SIAM Journal on Optimization (SIOPT)
The Institute is named after the famous Austrian mathematician Johann Radon (1887-1956)
Medieninhaber:
Österreichische Akademie der Wissenschaften
Juristische Person öffentlichen Rechts (BGBl 569/1921 idF BGBl I 130/2003)
Dr. Ignaz Seipel-Platz 2, 1010 Wien
Diese Website dient zur Information über die wissenschaftlichen Aktivitäten der Österreichischen Akademie der Wissenschaften und setzt somit den gesetzlichen Auftrag um, die Wissenschaft in jeder Hinsicht zu fördern.
This RICAM page was made with 100% valid HTML & CSS - Send comments to Webmaster
Today's date and time is 02/08/12 - 05:40 CET and this file ( /projects/PDE_Control_SQP/index.html ) was last modified on 06/23/08 - 11:20 CEST