Piermarco Cannarsa, Giuseppe Da Prato (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The vanishing viscosity method is adapted to the infinite dimensional case, by showing that the value function of a deterministic optimal control problem can be approximated by the solutions of suitable parabolic equations in Hilbert spaces.
Fabio Bagagiolo (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.
Di Marco, Silvia C., González, Roberto L.V. (2003)
International Journal of Mathematics and Mathematical Sciences
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Albert Altarovici, Olivier Bokanowski, Hasnaa Zidani (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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The paper deals with deterministic optimal control problems with state constraints and non-linear dynamics. It is known for such problems that the value function is in general discontinuous and its characterization by means of a Hamilton-Jacobi equation requires some controllability assumptions involving the dynamics and the set of state constraints. Here, we first adopt the viability point of view and look at the value function as its epigraph. Then, we prove that this epigraph can...
P. L. Lions (1985)
Banach Center Publications
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Piermarco Cannarsa, Giuseppe Da Prato (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
Piermarco Cannarsa, Giuseppe Da Prato (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
We prove an existence and uniqueness result for a class of Hamilton-Jacobi equations in Hilbert spaces.
Fabio Bagagiolo (2004)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We study a finite horizon problem for a system whose evolution is governed by a controlled ordinary differential equation, which takes also account of a hysteretic component: namely, the output of a Preisach operator of hysteresis. We derive a discontinuous infinite dimensional Hamilton–Jacobi equation and prove that, under fairly general hypotheses, the value function is the unique bounded and uniformly continuous viscosity solution of the corresponding Cauchy problem.
Giuseppe Da Prato, Jerzy Zabczyk (1997)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The Hamilton-Jacobi-Bellman equation corresponding to a large class of distributed control problems is reduced to a linear parabolic equation having a regular solution. A formula for the first derivative is obtained.
Salvatore Federico (2008)
Banach Center Publications
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In this paper we propose and study a continuous time stochastic model of optimal allocation for a defined contribution pension fund in the accumulation phase. The level of wealth is constrained to stay above a "solvency level". The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. The model is naturally formulated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach....
Alain Rapaport, Pierre Cartigny (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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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...