Special Topics in Continuous Optimization and Optimal Control: Local and Global convergence of Newton methods
Date:
In this seminar talk, we discussed the local and global convergence of Newton Methods topics which are under as follows:
- Lipschitz Condition, Contraction map, Convex set, Convex function
- Newton Methods: local convergence of Newton Methods, theorems, proof of quadratic convergence, and its advantages and drawbacks.
- Global convergence theorems, Banach Fixed Point Theorem, globalization schemes
- Modified Newton Method with Exact Line Search:
- Global Convergence Results for Modified Newton Method with Exact Line Search
- Modified Newton Method with Inexact Line Search:
- Global Convergence Results for Modified Newton Method with Inexact Line Search and their proofs
- Quasi Newton Methods:
- Global Convergence Results for Quasi-Newton Method (BFGS)
- Global Convergence Results for Quasi-Newton Method (A Subclass of Oren-Luenberger)
- Conclusions for Local- and Global- Properties of Newton Methods