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The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation.
K. Pearson, On Lines and Planes of Closest Fit to Systems of Points in Space
1901
Earlier work this paper cites.
V.G. Boltyanskii, R.V. Gamkrelidze. L.S. Pontryagin, Towards a theory of optimal processes, (Russian), Reports Acad. Sci. USSR, vol.110(1), 1956
1956
Earlier work this paper cites.
R. Bellman, Dynamic Programming. Princeton university press, Princeton, NJ, 1957
1957
Earlier work this paper cites.
R.A. Howard. Dynamic programming and Markov processes. Wiley, New York, 1960
1960
Earlier work this paper cites.
E. G. Al’brekht. On the optimal stabilization of nonlinear systems,
1961
Earlier work this paper cites.
L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, The Mathematical Theory of Optimal Processes (Russian), English translation: Interscience 1962
1962
Earlier work this paper cites.
R. P. Brent, Algorithms for Minimization without Derivatives, Prentice-Hall, Englewood Cliffs, New Jersey, 1973
1973
Earlier work this paper cites.
W.H. Fleming, H.M. Soner, Controlled Markov processes and viscosity solutions, Springer–Verlag, New York, 1993
1993
Earlier work this paper cites.
F. Camilli, M. Falcone, P. Lanucara, and A. Seghini. A domain decomposition method for Bellman equations
1994
Earlier work this paper cites.
M. Falcone, P. Lanucara, and A. Seghini. A splitting algorithm for Hamilton-Jacobi-Bellman equations
1994
Earlier work this paper cites.
M. Bardi and I. Capuzzo-Dolcetta. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Basel, 1997
1997
Earlier work this paper cites.
M. Falcone, T. Giorgi, An approximation scheme for evolutive Hamilton-Jacobi equations
1999
Cited alongside, same era.
A. Quarteroni and A. Valli. Domain Decomposition Methods for Partial Differential Equations, Oxford University Press, 1999
1999
Cited alongside, same era.
J. A. Sethian. Level set methods and fast marching methods
1999
Cited alongside, same era.
I.T. Jolliffe, Principal component analysis, Springer Series in Statistics, 2nd ed., Springer, 2002
2002
Cited alongside, same era.
S. Osher, R. Fedkiw, Level Set Methods and Dynamic Implicit Surfaces, Springer, 2003
2003
Cited alongside, same era.
E. Carlini, M. Falcone and R. Ferretti, An efficient algorithm for Hamilton-Jacobi equations in high dimension
S. Cacace, E. Cristiani. M. Falcone, and A. Picarelli. A patchy dynamic programming scheme for a class of Hamilton-Jacobi-Bellman equations
2012
Later among the works it cites.
M. Falcone and R. Ferretti. Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi equations, SIAM, 2013
2013
Later among the works it cites.
S. Volkwein. Model Reduction using Proper Orthogonal Decomposition
2013
Later among the works it cites.
A. Alla, M. Falcone, and D. Kalise. An efficient policy iteration algorithm for dynamic programming equations
2015
Later among the works it cites.
A. Festa. Reconstruction of independent sub-domains for a class of Hamilton–Jacobi equations and application to parallel computing
2016
Later among the works it cites.
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2004
Cited alongside, same era.
K. Kunisch, S. Volkwein, and L. Xie. HJB-POD based feedback design for the optimal control of evolution problems
2004
Cited alongside, same era.
C. Navasca and A.J. Krener. Patchy solutions of Hamilton-Jacobi-Bellman partial differential equations
2007
Cited alongside, same era.
M. Hinze, R. Pinnau, M. Ulbrich, and S. Ulbrich. Optimization with PDE Constraints. Mathematical Modelling: Theory and Applications, 23
2009
Cited alongside, same era.
C.L. Evans. Partial Differential Equations. American Mathematical Society, 2010
2010
Cited alongside, same era.
F. Tröltzsch. Optimal Control of Partial Differential Equations: Theory, Methods and Application, American Mathematical Society, 2010
2010
Cited alongside, same era.
A. Alla, M. Falcone, S. Volkwein, Error analysis for POD approximations of infinite horizon problems via the dynamic programming approach
Cited in the paper.
D. Kalise, A. Kroener and K. Kunisch, Local minimization algorithms for dynamic programming equations
2016
Later among the works it cites.
J. Garcke and A. Kröner. Suboptimal feedback control of PDEs by solving HJB equations on adaptive sparse grids
2017
Later among the works it cites.
A. Festa, Domain decomposition based parallel Howard’s algorithm
2018
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D. Kalise, K. Kunisch, Polynomial approximation of high-dimensional Hamilton-Jacobi-Bellman equations and applications to feedback control of semilinear parabolic PDEs
2018
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