Narzędzia help

Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
first previous next last
cannonical link button

http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-BSW3-0045-0002

Czasopismo

Archives of Control Sciences

Tytuł artykułu

A new stopping criterion for iterative solvers for control optimal problems

Autorzy Krumbiegel, K.  Rosch, A. 
Treść / Zawartość http://www.degruyter.com/view/j/acsc http://journals.pan.pl/dlibra/journal/96936
Warianty tytułu
Języki publikacji EN
Abstrakty
EN Linear quadratic optimal control problems governed by PDEs with pointwise control constraints are considered. We derive error estimates for feasible and infeasible controls of the problem. Based on this theory an error estimator is constructed for different discretization schemes. Moreo ver, we establish the estimator as a stopping criterion for several optimization methods. Furthermore, additional errors caused by solving the linear systems are discussed. The theory is illustrated by numerical examples.
Słowa kluczowe
EN linear quadratic optimal control problems   control constraints   error estimates   projected gradient method   primal-dual active set strategy   penalty methods   stopping criteria  
Wydawca Polish Academy of Sciences, Committee of Automation and Robotics
Czasopismo Archives of Control Sciences
Rocznik 2008
Tom Vol. 18, no. 1
Strony 17--42
Opis fizyczny Bibliogr. 19 poz., rys., tab.
Twórcy
autor Krumbiegel, K.
autor Rosch, A.
Bibliografia
[1] N. ARADA, E. CASAS and F. TROLTZSCH: Error estimates for a emilinear elliptic optimal control problem. Computional Optimization and Approximation, 23 (2002), 201-229.
[2] M. BERGOUNIOUX, K. ITO and K. KUNISCH: Primal-dual strategy for constrained optimal control problems. SIAM J. Control and Optimization, 37 (1999), 1176-1194.
[3] D. P. BERTSEKAS: Constrained optimization and Lagrange multiplier methods. (Computer Science and Applied Mathematics), New York, 1982.
[4] J. T. BETTS: Very low-thrust trajectory optimization using a direct S QP method. J. Computational and Applied Mathematics, 120(1-2), (2000), 27-40.
[5] H. G. BOCK, W. EGARTNER, W. KAPPIS and V. SCHULZ: Practical shape optimization for turbine and compressor blades by the use of PRSQP methods. Optimization and Engineering, 3(4), (2003), 395-414.
[6] R. FALK: Approximation of a class of optimal control problems with order of convergence estimates. J. Math. Anal. Appl., 44 (1973), 28-47.
[7] C. GEIGER and C. KANZOW: Theory and numerical algorithms for contranined optimization problems. (Theorie and Numerik restringierter Optimierungsaufgaben). Springer-Verlag, Berlin, 2002, (in German).
[8] T. GEVECI: On the approximation of the solution of an optimal control problem governed by an elliptic equation. R.A.I.R.O. Analyse numerique, 13 (1979), 313-328.
[9] C. GROSSMANN and A . A. KAPLAN: On the solution of discretized obstacle problems by an adapted penalty method. Computing, 35 (1985), 295-306.
[10] M. HINTERMULLER, K. ITO and K. KUNISCH: The primal-dual active set method as a semi-smooth Newton method. SIAM J. Optimization, 13 (2003), 865-888.
[11] M. HINTERMOLLER and M. ULBRICH: A mesh-independence result for semismooth newton methods. Mathematical Programming, 101(1), (2004), 151-184.
[12] M. HINZE: A variational discretization concept in control constrained optimization: The linearquadratic case. Computational Optimization and Applications, 30 (2005), 45-61.
[13] K. KUNISCH and A. ROSCH: Primal-dual active set strategy for a general class of constrained optimal control problems. SIAM J. Optimization, 13(2), (2002), 321-334.
[14] F. LEIBFRITZ and E .W. SACHS: Inexact SQP interior point methods and large scale optimal control problems. SIAM J. on Control and Optimization, 38(1), (1999), 272-293.
[15] K. MALANOWSKI: Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal control problems. Appl. Math. Opt., 8 (1981), 69-95.
[16] C. MEYER and A. ROSCH: Superconvergence properties of optimal control problems. SIAM J. Control and Optimization, 43(3), (2004), 970-985.
[17] A. SCHIELA and M. WEISER: Function space interior point methods for pde constrained optimization. PAMM, 4 (2004), 43-46.
[18] F. TRÖLTZSCH: Optimal control of partial differentiable systems - Theory, methods and applications (Optimale Steuerung partieller Differentialgleichungen - Theorie, Verfahren and Anwendungen). Vieweg, Wiesbaden, 2005, (in German).
[19] M. ULBRICH: Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim., 13 (2003), 805-842.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-article-BSW3-0045-0002
Identyfikatory