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- Legendre–Clebsch_condition abstract "In the calculus of variations the Legendre–Clebsch condition is a second-order condition which a solution of the Euler–Lagrange equation must satisfy in order to be a maximum (and not a minimum or another kind of extremal).For the problem of maximizingthe condition isIn optimal control, the situation is more complicated because of the possibility of a singular solution. The generalized Legendre–Clebsch condition, also known as convexity, is a sufficient condition for local optimality such that when the linear sensitivity of the Hamiltonian to changes in u is zero, i.e., The Hessian of the Hamiltonian is positive definite along the trajectory of the solution: In words, the generalized LC condition guarantees that over a singular arc, the Hamiltonian is minimized.".
- Legendre–Clebsch_condition wikiPageID "18409176".
- Legendre–Clebsch_condition wikiPageRevisionID "599292196".
- Legendre–Clebsch_condition subject Category:Calculus_of_variations.
- Legendre–Clebsch_condition subject Category:Optimal_control.
- Legendre–Clebsch_condition comment "In the calculus of variations the Legendre–Clebsch condition is a second-order condition which a solution of the Euler–Lagrange equation must satisfy in order to be a maximum (and not a minimum or another kind of extremal).For the problem of maximizingthe condition isIn optimal control, the situation is more complicated because of the possibility of a singular solution.".
- Legendre–Clebsch_condition label "Legendre–Clebsch condition".
- Legendre–Clebsch_condition sameAs Legendre%E2%80%93Clebsch_condition.
- Legendre–Clebsch_condition sameAs Q6517889.
- Legendre–Clebsch_condition sameAs Q6517889.
- Legendre–Clebsch_condition wasDerivedFrom Legendre–Clebsch_condition?oldid=599292196.