Extending the level proximal subdifferential

Many real-world applications can be modeled as nonconvex optimization problems, such as the phase retrieval problem in medical imaging and matrix factorization problems in data analysis, just to name a few. Proximal-type algorithms serve as ideal candidates to resolve these nonconvex problems. Nevertheless, their convergence analysis remains challenging due to the lack of favorable properties and a uniform framework. Developing the novel extension of the level proximal subdifferential will enhance the mathematical foundation of proximal-type algorithms in the absence of convexity, anticipated to provide a uniform framework for the convergence analysis of these algorithms. As such, this project will bring new insights about the behavior of proximal-type algorithms for the nonconvex optimization problems, fostering better algorithmic solutions to computational challenges arisen from real-world scientific applications.

Faculty Supervisor:

Shawn Wang

Student:

Partner:

Kyushu University

Discipline:

Mathematics

Sector:

Education

University:

The University of British Columbia - Okanagan

Program: