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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 maximizing : the condition is : ==Generalized Legendre-Clebsch== In optimal control, the situation is more complicated because of the possibility of a singular solution. The generalized Legendre–Clebsch condition,〔H.M. Robbins, A generalized Legendre-Clebsch condition for the singular cases of optimal control, IBM Journal of Research and Development, 1967〕 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Legendre–Clebsch condition」の詳細全文を読む スポンサード リンク
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