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Hessian Operators on Constraint Manifolds

Birtea, Petre ; Comănescu, Dan

Journal of Nonlinear Science, 2015, Vol.25(6), pp.1285-1305 [Periódico revisado por pares]

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  • Título:
    Hessian Operators on Constraint Manifolds
  • Autor: Birtea, Petre ; Comănescu, Dan
  • Assuntos: Hessian operator ; Riemannian manifolds ; Optimization ; Orthogonal group ; Nonlinear stability
  • É parte de: Journal of Nonlinear Science, 2015, Vol.25(6), pp.1285-1305
  • Descrição: On a constraint manifold we give an explicit formula for the Hessian matrix of a cost function that involves the Hessian matrix of a prolonged function and the Hessian matrices of the constraint functions. We give an explicit formula for the case of the orthogonal group mathbf{O}(n) O ( n ) by using only Euclidean coordinates on \mathbb {R}}^{n^2} R n 2 . An optimization problem on mathbf{SO}(3) SO ( 3 ) is completely carried out. Its applications to nonlinear stability problems are also analyzed.
  • Idioma: Inglês

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