2019
Chapter
Communications in Computer and Information Science
Springer
Evgeni Nurminski, Natalia Shamray Discrete Time Lyapunov-Type Convergence Conditions for Recurrent Sequences in Optimization and Subgradient Method for Weakly Convex Functions // Mathematical Optimization Theory and Operations Research. 18th International Conference, MOTOR 2019, Ekaterinburg, Russia, July 8 - 12, 2019. Revised Selected Papers. Springer, Communications in Computer and Information Science (CCIS). Volume 1090. P.294-303
We present here the set of conditions for recursive optimization-like processes which guarantee their convergence to a given solution set. These conditions simplify convergence studies for such processes by essentially reducing them to the analysis of the processes behavior at arbitrary small vicinity of points outside the solution set. They also implicitly implement a rather complicated part of the logic of convergence proofs when there is no strict monotonicity of Lyapunov function along the process trajectory.