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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, we try to find a correction that decreases the energy of the nonlinear functional of the current iterate x. The correction is calculated using the Taylor expansion around x, resulting in the problem: Hessian(x) * correction = -gradient(x). Within a certain radius around x, the functional can be approximated correctly and then the corrections causes an energy decrease. 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.
Lisa Julia Nebel authoredAdd first version of the Riemannian Proximal Newton solver, as an alternative to the Trust-Region Solver. In each step of these two iterative solvers, we try to find a correction that decreases the energy of the nonlinear functional of the current iterate x. The correction is calculated using the Taylor expansion around x, resulting in the problem: Hessian(x) * correction = -gradient(x). Within a certain radius around x, the functional can be approximated correctly and then the corrections causes an energy decrease. 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.