Geodesic
Turnpike theorems by a value function approach
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 123-141

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Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness of the singular solution. We provide a new necessary and sufficient condition for turnpike optimality, even in the presence of multiple singular solutions.

DOI : 10.1051/cocv:2003039
Classification : 34H05, 49K05, 49L25
Keywords: calculus of variations, infinite horizon, Hamilton-Jacobi equation, viscosity solutions, turnpike 
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     author = {Rapaport, Alain and Cartigny, Pierre},
     title = {Turnpike theorems by a value function approach},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {123--141},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {1},
     year = {2004},
     doi = {10.1051/cocv:2003039},
     mrnumber = {2084258},
     zbl = {1068.49016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003039/}
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Rapaport, Alain; Cartigny, Pierre. Turnpike theorems by a value function approach. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 123-141. doi: 10.1051/cocv:2003039

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