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Lisa Julia Nebel
authored
Add first version of the Riemannian Proximal Newton solver, as an alternative to the Trust Region Solver. In each step of these two iterative solvers: For a given iterate x, we try to find a correction that decreases the energy of the nonlinear functional. This correction is calculated using the Taylor expansion around x, resulting in the problem: Hessian(x) * correction = -gradient(x). The correction only causes an energy decrease if the functional can be approximated correctly within a certain radius around x. 1) The trust-region algorithm ensures this using a trust-region. 2) The proximal newton method ensures this by "punishing" large corrections using a regularization factor.
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