Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Semilinear elliptic optimal control problems with pointwise control and mixed control-state constraints are considered. Necessary and sufficient optimality conditions are given. The equivalence of the SQP method and Newton's method for a generalized equation is discussed. Local quadratic convergence of the SQP method is proved.
Czasopismo
Rocznik
Tom
Strony
717--738
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
autor
autor
- TU Chemnitz, Faculty of Mathematics, D-09107 Chemnitz, Germany, roland.griesse@mathematik.tu-chemnitz.de
Bibliografia
- ADAMS, R. (1975) Sobolev Spaces. Pure and Applied Mathematics 65. Academic Press, New York-London.
- ALT, W. (1990) The Lagrange-Newton method for infinite-dimensional optimization problems. Numerical Functional Analysis and Optimization, 11, 201-224.
- ALT, W. (1994) Local convergence of the Lagrange-Newton method with applications to optimal control. Control & Cybernetics, 23(1-2), 87-105.
- ALT, W., GRIESSE, R., METLA, N. and RÖSCH, A. (2010) Lipschitz stability for elliptic optimal control problems with mixed control-state constraints. Optimization, 59(6), 833-849.
- ALT, W. and MALANOWSKI, K. (1993) The Lagrange-Newton method for non-linear optimal control problems. Computational Optimization and Applications. An International Journal, 2(1), 77-100.
- ALT, W., SONTAG, R. and TRÖLTZSCH, F. (1996) An SQP method for optimal control of weakly singular Hammerstein integral equations. Appl. Math. Optim., 33(3), 227-252.
- DOKOV, S.P. and DONTCHEV, A.L. (1998) Robinson's strong regularity implies robust local convergence of Newton’s method. In: Optimal control (Gainesville, FL, 1997), Appl. Optim., Kluwer Acad. Publ., Dordrecht, 15, 116-129.
- DONTCHEV, A. (1995) Implicit function theorems for generalized equations. Mathematical Programming, 70, 91-106.
- GRIESSE, R., METLA, N. and RÖSCH, A. (2008) Local quadratic convergence of SQP for elliptic optimal control problems with mixed control-state constraints. RJCAM Report 2008-21, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences,Linz, Austria, http://www.ricam.oeaw.ac.at/publications/ reports/08/rep08-21.pdf.
- GRIESSE, R. and WACHSMUTH, D. (2009) Sensitivity analysis and the adjoint update strategy for optimal control problems with mixed control-state constraints. Computational Optimization and Applications, 44(1), 57-81.
- GRISVARD, P. (1985) Elliptic Problems in Nonsmooth Domains. Pitman, Boston.
- HEINKENSCHLOSS, M. (1998) Formulation and analysis of a sequential qua¬dratic programming method for the optimal Dirichlet boundary control of Navier-Stokes flow. In: Optimal Control (Gainesville, FL, 1997), Applied Optimization, Kluwer Academic Publishers, Boston, 15, 178-203.
- HEINKENSCHLOSS, M. and TRÖLTZSCH, F. (1998) Analysis of the Lagrange-SQP-Newton Method for the Control of a Phase-Field Equation. Control & Cybernetics, 28, 177-211.
- MALANOWSKI, K. (1996) Convergence of Lagrange-Newton method for control-state and pure state constrained optimal control problems. In: System modelling and optimization (Prague, 1995). Chapman & Hall, London, 419-426.
- MALANOWSKI, K. (2001) Stability and sensitivity analysis for optimal control problems with control-state constraints. Dissertationes Mathematicae (Rozprawy Matematyczne), 394.
- MALANOWSKI, K. (2004) Convergence of the Lagrange-Newton method for optimal control problems. International Journal of Applied Mathematics and Computer Science, 14(4), 531-540.
- MAURER, H. (1981) First and second order sufficient optimality conditions in mathematical programming and optimal control. Mathematical Programming Study, 14, 163-177.
- MAURER, H. and ZOWE, J. (1979) First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems. Mathematical Programming, 16, 98-110.
- MEYER, C., PRÜFERT,U. and TRÖLTZSCH, F. (2007) On two numerical methods for state-constrained elliptic control problems. Optimization Methods and Software, 22(6), 871-899.
- MEYER, C., RÖSCH, A. and TRÖLTZSCH, F. (2005) Optimal control of PDEs with regularized pointwise state constraints. Computational Optimization and Applications, 33(2-3), 209-228.
- MEYER, C. and TRÖLTZSCH, F. (2006) On an elliptic optimal control problem with pointwise mixed control-state constraints. In: A. Seeger, ed., Recent Advances in Optimization. Proceedings of the 12th French-German-Spanish Conference on Optimization. LNEMS 563, Springer, New York, 187-204.
- ROBINSON, S. (1980) Strongly regular generalized equations. Mathematics of Operations Research, 5(1), 43-62.
- RÖSCH, A. and TRÖLTZSCH, F. (2003) Sufficient second-order optimality conditions for a parabolic optimal control problem with pointwise control-state constraints. SI AM Journal on Control and Optimization, 42(1), 138-154.
- RÖSCH, A. and TRÖLTZSCH, F. (2006a) Existence of regular Lagrange multipliers for elliptic optimal control problems with pointwise control-state constraints. SIAM Journal on Control and Optimization, 45(2), 548-564.
- RÖSCH, A. and TRÖLTZSCH, F. (2006b) Sufficient second-order optimality conditions for an elliptic optimal control problem with pointwise control-state constraints. SIAM Journal on Optimization, 17(3), 776-794.
- RÖSCH, A. and TRÖLTZSCH, F. (2007) On regularity of solutions and Lagrange multipliers of optimal control problems for semilinear equations with mixed pointwise control-state constraints. SIAM Journal on Control and Optimization, 46(3), 1098-1115.
- TRÖLTZSCH, F. (1994) An SQP method for optimal control of a nonlinear heat equation. Control & Cybernetics, 23, 267-288.
- TRÖLTZSCH, F. (1999) On the Lagrange-Newton-SQP method for the optimal control of semilinear parabolic equations. SIAM Journal on Control and Optimization, 38(1), 294-312.
- TRÖLTZSCH, F. (2005) Optimale Steuerung partieller Differentialgleichungen. Theorie, Verfahren und Anwendungen. Vieweg, Wiesbaden.
- TRÖLTZSCH, F. and VOLKWEIN, S. (2001) The SQP method for control constrained optimal control of the Burgers equation. ESAIM: Control, Optimisation and Calculus of Variations, 6, 649-674.
- TRÖLTZSCH, F. and WACHSMUTH, D. (2006) Secondorder sufficient optimality conditions for the optimal control of Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, 12(1), 93-119.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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