This project focuses on methods that smartly exploit the special structure of the constraint set (as a solution set of another optimization problem) and involves explicit operations for solving bi-level optimization problems. Among several theoretical results, we have provided in recent papers, the convergence rate result of the sequence of function values is special since it is the first of its kind. This area of research is thriving for new algorithms for tackling various bi-level problems.
This project focuses on the design, analysis, development, and practical implementation of simple algorithms for solving the Wireless Sensor Network (WSN) Localization problems. In a recent paper, we solve the original non-convex and non-smooth formulation using first-order methods. We proposed a parameter-free algorithmic framework that includes the whole spectrum ranging from a fully centralized to a fully distributed implementation, and that it can also achieve partial parallelization.
In this project, we address a structured deep learning optimization problems, which are given by the sum of non-convex and non-smooth functions. As an example, we study a particular case of structure where the non-smoothness is represented as the maximum of non-convex smooth functions. Recently, for the structure of maximum, we have developed, the Stochastic Proximal Linear Method (SPLM) that is guaranteed to reach a critical point of this learning objective and analyze its convergence rate.