Lec 24: Banach Contraction Mapping Theorem and Convergence Analysis

In this lecture on Nonlinear Programming, we explore the Banach Contraction Mapping Theorem and its application to the convergence of optimization algorithms. We will cover the basics of the theorem, how it applies to optimization problems, and how it can be used to analyze the convergence of iterative optimization algorithms. Join us for a deep dive into the mathematical foundations of optimization algorithms and learn how to leverage the Banach Contraction Mapping Theorem for estbalishing convergence of optimization algorithms.

This lecture series is from the Nonlinear Programming course that ran at The Ohio State University under the course number ECE 5759. The course builds on linear algebra and calculus to derive various algorithms for optimization in static and dynamic systems. The course is aimed at first-year graduate students, though senior undergraduate students with advanced knowledge of mathematics can also grasp the concepts discussed in the course.
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