Abstract estimates of the rate of convergence for optimal control problems

Tommi Kärkkäinen1, Tiina Räisänen1
1Department of Mathematics, Laboratory of Scientific Computing, University of Jyväskylä, Jyväskylä, Finland

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H. T. Banks and K. Kunisch (1989) Estimation Techniques for Distributed Parameter Systems, volume 1 of Systems & Control: Foundations & Applications. Birkhäuser, Boston

D. P. Bertsekas (1982) Constrained Optimization and Lagrange Multiplier Methods. Computer Science and Applied Mathematics. Academic Press, New York

J. H. Bramble and R. Scott (1978) Simultaneous approximation in scales of Banach spaces. Math. Comp., 32:947–954

S. C. Brenner and L. R. Scott (1994) The Mathematical Theory of Finite Element Methods, volume 15 of Texts in Applied Mathematics. Springer-Verlag, New York

R. H. Byrd, P. Lu, J. Nocedal, and C. Zhu (1994) A limited memory algorithm for bound constrained optimization. Technical Report NAM-08, Department of Electrical Engineering and Computer Science, Northwestern University

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang (1988) Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer-Verlag, New York

P. G. Ciarlet (1978) The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam

P. G. Ciarlet and J. L. Lions, editors (1991) Finite Element Methods (Part 1), volume 2. Elsevier, North-Holland, Amsterdam

R. S. Falk (1973) Approximation of a class of optimal control problems with order of convergence estimates. J. Math. Anal. Appl., 44:28–47

D. A. French and J. T. King (1991) Approximation of an elliptic control problem by the finite element method. Numer. Funct. Anal. Optim., 12:299–314

M. Křížek and P. Neittaanmäki (1990) Finite Element Approximation of Variational Problems and Applications, volume 50 of Pitman Monographs and Surveys in Pure and Applied Mathematics. Longman, Essex

I. Lasiecka (1984) Ritz-Galerkin approximation of the time optimal boundary control problem for parabolic systems with Dirichlet boundary conditions. SIAM J. Control Optim., 22:477–500

J. L. Lions (1971) Optimal Control of Systems Governed by Partial Differential Equations, volume 170 of Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Springer-Verlag, Berlin

K. Malanowski (1981) Convergence of approximations vs. regularity of solutions for convex, control-constrained optimal-control problems. Appl. Math. Optim., 8:69–95

P. Neittaanmäki and D. Tiba (1994) Optimal Control of Nonlinear Parabolic Systems; Theory, Algorithms, and Applications. Pure and Applied Mathematics. Marcel Dekker, New York

A. Quarteroni and A. Valli (1994) Numerical Approximation of Partial Differential Equations. Number 23 in Springer Series in Computational Mathematics. Springer-Verlag, Berlin

D. Tiba (1995) Lectures on the Optimal Control of Elliptic Equations. Lecture Notes 32. Department of Mathematics, University of Jyväskylä

E. Zeidler (1990) Nonlinear Functional Analysis and its Applications; II/B: Nonlinear Monotone Operators. Springer-Verlag, Berlin