Asymptotic Dynamics of Alternating Minimization for Non-Convex Optimization

This study investigates the asymptotic dynamics of alternating minimization applied to optimize a bilinear non-convex function with normally distributed covariates. We employ the replica method from statistical physics in a multi-step approach to precisely trace the algorithm's evolution. Our findings indicate that the dynamics can be described effectively by a two--dimensional discrete stochastic process, where each step depends on all previous time steps, revealing a memory dependency in the procedure. The theoretical framework developed in this work is broadly applicable …

algorithm cond-mat.dis-nn distributed dynamics evolution function math.oc normally optimization physics replica statistical stat.ml study the algorithm