All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 57

Showing per page

Monotonicity properties of minimizers and relaxation for autonomous variational problems

Giovanni Cupini, Cristina Marcelli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the following classical autonomous variational problem minimize F ( v ) = ∫ a b f ( v ( x ) , v ' ( x ) ) x ̣ : v ∈ A C ( [ a , b ] ) , v ( a ) = α , v ( b ) = β , where the Lagrangian f is possibly neither continuous, nor convex, nor coercive. We prove a monotonicity property of the minimizers stating that they satisfy the maximum principle or the minimum one. By virtue of such a property, applying recent results concerning constrained variational problems, we derive a relaxation theorem, the DuBois-Reymond necessary condition and some existence or non-existence criteria.

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Currently displaying 21 – 40 of 57