Abstract
In the paper, the behaviour of variable metric methods along geodesics is analyzed. First, a general framework is given in the case of Riemannian submanifolds in R n, then two general convergence theorems for a wide class of nonlinear optimization methods are proved to find a stationary point or a local optimum point of a smooth function defined on a compact set of a Riemannian manifold and the rate of a convergence is studied. These methods and theorems should be extended in such a way that penalty methods be generalized in the case of inequality constraints defined on Riemannian manifolds.
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Rapcsák, T. (1998). Variable metric methods along geodetics. In: Giannessi, F., Komlósi, S., Rapcsák, T. (eds) New Trends in Mathematical Programming. Applied Optimization, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2878-1_19
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DOI: https://doi.org/10.1007/978-1-4757-2878-1_19
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