Convergence Rates of Inertial Splitting Schemes for Nonconvex Composite Optimization

Understand

We study the convergence properties of a general inertial first-order proximal splitting algorithm for solving nonconvex nonsmooth optimization problems.

• Using the Kurdyka--\L ojaziewicz (KL) inequality we establish new convergence rates which apply to several inertial algorithms in the literature.
• Our basic assumption is that the objective function is semialgebraic, which lends our results broad applicability in the fields of signal processing and machine learning.
• The convergence rates depend on the exponent of the "desingularizing function" arising in the KL inequality.