A composite step method for equality constrained optimization on manifolds

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Ortiz, Julián ; Schiela, Anton:
A composite step method for equality constrained optimization on manifolds.
Bayreuth , 2019 . - 27 S.

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Abstract

We present a composite step method, designed for equality constrained optimization on differentiable manifolds. The use of retractions allows us to pullback the involved mappings to linear spaces and use tools such as cubic regularization of the objective function and affine covariant damped Newton method for feasibility. We show fast local convergence when different chart retractions are considered. We test our method on equilibrium problems in finite elasticity where the stable equilibrium position of an inextensible transversely isotropic elastic rod under dead load is searched.