Project
Proximal Algorithms for Structured Nonconvex Optimization
Although proximal algorithms are widely used in engineering applications, there is no satisfactory theory in support of their employment for nonconvex problems, and their efficacy is severely affected by ill conditioning. The thesis aims at overcoming these downsides by proposing a novel universal framework for the convergence analysis of nonconvex and nonsmooth proximal algorithms. It also enables the possibility to employ quasi-Newton methods to robustify them against ill conditioning and dramatically increase their accuracy. These enhancements 1) preserve complexity and convergence properties of the underlying proximal algorithm, 2) are suited for nonconvex problems, and 3) achieve asymptotic superlinear rates under assumptions only at the limit point.