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arXiv · 1403.4091

Hessian Operators on Constraint Manifolds

Petre Birtea·Dan Comănescu
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Abstract

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 ${\bf O}(n)$ by using only Euclidean coordinates on $\mathbb{R}^{n^2}$. An optimization problem on ${\bf SO}(3)$ is completely carried out. Its applications to nonlinear stability problems are also analyzed.

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Petre Birtea, Dan Comănescu. 2014-03-17. Hessian Operators on Constraint Manifolds. https://doi.org/10.1007/s00332-015-9256-7

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