Hessian Informed Mirror Descent

Inspired by the recent paper (L. Ying, Journal of Scientific Computing, 84, 1–14 (2020), we explore relationship between mirror descent and variable metric method. When in decent is induced a convex function, whose Hessian close to objective this method enjoys both robustness from superlinear convergence for Newton type methods. applied linearly constrained minimization problem, prove global local convergence, continuous discrete settings. As applications, compute Wasserstein gradient flows Cahn-Hillard equation with degenerate mobility. formulating these problems using minimizing movement scheme respect metric, our algorithm offers fast speed underlying optimization problem while maintaining total mass bounds solution.