2021/09/12 by Renbo Zhao, Zhao, Renbo · 1 citation
Computer Science · Engineering · Materials Science · #FOS: Mathematics #Graphene research and applications #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2109.05601
openalex publication_date 2021/09/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We analyze the convergence rate of the multiplicative gradient (MG) method for PET-type problems with m component functions and an n-dimensional optimization variable. We show that the MG method has an O(ln(n)/t) convergence rate, in both the ergodic and the non-ergodic senses. Furthermore, we show that the distances from the iterates to the set of optimal solutions converge (to zero) at rate O(1/√(t)). Our results show that, in the regime n=O(exp(m)), to find an ε-optimal solution of the PET-type problems, the MG method has a lower computational complexity compared with the relatively-smooth gradient method and the Frank-Wolfe method for convex composite optimization involving a logarithmically-homogeneous barrier.