Mathematical Optimization for Data Science Group, Saarland University

Welcome to the homepage of the

Mathematical Optimization for Data Science Group

Department of Mathematics and Computer Science, Saarland University, Germany

Home
Teaching
Research
Publications
Job Offers

Saarland
University

Mathematics
and

Computer Science

Global Convergence of Model Function Based Bregman Proximal Minimization Algorithms

M.C. Mukkamala, J. Fadili and P. Ochs

Abstract:
Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix factorization or deep neural network problems do not have a Lipschitz continuous gradient. This led to the development of a generalized notion known as the L-smad property, which is based on generalized proximity measures called Bregman distances. However, the L-smad property cannot handle nonsmooth functions, for example, simple nonsmooth functions like |x^4-1| and also many practical composite problems are out of scope. We fix this issue by proposing the MAP property, which generalizes the L-smad property and is also valid for a large class of nonconvex nonsmooth composite problems. Based on the proposed MAP property, we propose a globally convergent algorithm called Model BPG, that unifies several existing algorithms. The convergence analysis is based on a new Lyapunov function. We also numerically illustrate the superior performance of Model BPG on standard phase retrieval problems, robust phase retrieval problems, and Poisson linear inverse problems, when compared to a state of the art optimization method that is valid for generic nonconvex nonsmooth optimization problems.



pdf	Bibtex	Publisher's link	arXiv

Latest update: 24.12.2020

Citation:
M.C. Mukkamala, J. Fadili, P. Ochs:
Global Convergence of Model Function Based Bregman Proximal Minimization Algorithms.

Journal of Global Optimization, 83:753-781, 2022.

Bibtex:
@article{MFO22, title = {Global Convergence of Model Function Based Bregman Proximal Minimization Algorithms}, author = {M.C. Mukkamala and J. Fadili and P. Ochs}, year = {2022}, journal = {Journal of Global Optimization}, volume = {83}, pages = {753--781} }

Impressum
Datenschutz