Convergence of the time-discretized monotonic schemes

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1. A.D. Bandrauk and H. Shen, Exponential split operator methods for solving coupled time-dependent Schrödinger equations. J. Chem. Phys.99 (1993) 1185–1193.  
2. K. Beauchard, Local controllability of a 1D Schrödinger equation. J. Math. Pures Appl.84 (2005) 851–956.  
3. J. Bolte and H. Attouch, On the convergence of the proximal point algorithm for nonsmooth functions involving analytic features. Math. Program. (to appear).  
4. E. Brown and H. Rabitz, Some mathematical and algorithmic challenges in the control of quantum dynamics phenomena. J. Math. Chem.31 (2002) 17–63.  
5. A. Haraux, M.A. Jendoubi and O. Kavian, Rate of decay to equilibrium in some semilinear parabolic equations. J. Evol. Equ.3 (2003) 463–484.  
6. K. Ito and K. Kunisch, Optimal bilinear control of an abstract Schrödinger equation. SIAM J. Cont. Opt. (to appear).  
7. R. Judson and H. Rabitz, Teaching lasers to control molecules. Phys. Rev. Lett68 10 (1992) 1500–1503.  
8. S. Łojasiewicz, Une propriété topologique des sous-ensembles analytiques réels. Colloques internationaux du CNRS, Les équations aux dérivées partielles117 (1963).  
9. S. Łojasiewicz, Sur la géométrie semi- et sous-analytique. Ann. Inst. Fourier43 (1993) 1575–1595.  
10. Y. Maday and G. Turinici, New formulations of monotonically convergent quantum control algorithms. J. Chem. Phys118 18 (2003) 8191–8196.  
11. Y. Maday, J. Salomon and G. Turinici, Discretely monotonically convergent algorithm in quantum control, in Proc. LHMNLC03 IFAC conference, Sevilla (2003) 321–324.  
12. Y. Maday, J. Salomon and G. Turinici, Monotonic time-discretized schemes in quantum control. Num. Math.103 (2006) 323–338.  
13. H. Rabitz, G. Turinici and E. Brown, Control of quantum dynamics: Concepts, procedures and future prospects, in Computational Chemistry, Special Volume (C. Le Bris Editor) of Handbook of Numerical Analysis, Vol. X, edited by Ph.G. Ciarlet, Elsevier Science B.V. (2003).  
14. J. Salomon, Limit points of the monotonic schemes in quantum control, in Proc. 44th IEEE Conference on Decision and Control, Sevilla (2005).  
15. S. Shi, A. Woody and H. Rabitz, Optimal control of selective vibrational excitation in harmonic linear chain molecules. J. Chem. Phys.88 (1988) 6870–6883.  
16. G. Strang, Accurate partial difference methods. I: Linear cauchy problems. Arch. Rat. Mech. An.12 (1963) 392–402.  
17. J. Szeftel, Absorbing boundary conditions for nonlinear Schrödinger equation. Num. Math.104 (2006) 103–127.  
18. D. Tannor, V. Kazakov and V. Orlov, Control of photochemical branching: Novel procedures for finding optimal pulses and global upper bounds, in Time Dependent Quantum Molecular Dynamics, J. Broeckhove, L. Lathouwers Eds., Plenum (1992) 347–360.  
19. T.N. Truong, J.J. Tanner, P. Bala, J.A. McCammon, D.J. Kouri, B. Lesyng and D.K. Hoffman, A comparative study of time dependent quantum mechanical wave packet evolution methods. J. Chem. Phys.96 (1992) 2077–2084.  
20. W. Zhu and H. Rabitz, A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator. J. Chem. Phys.109 (1998) 385–391.  

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