Adam B. Levy Books

The book delves into numerical minimization techniques for optimization problems, introducing multiset-mappings to enhance iteration mapping processes. It extends concepts from numerical variational analysis to explore continuity and differentiability of these mappings, along with proving a fixed-point theorem. By integrating ideas from dynamical systems, the text develops concepts of basin size and basin entropy. Additionally, it includes simulations for estimating basins of attraction, measuring basin size, and analyzing convergence behavior in numerical minimization.

The book presents a comprehensive framework for various numerical optimization methods through its "reduce-or-retreat" approach, which balances reducing the objective at trial points with retreating to closer alternatives. It aligns derivative-based methods, fostering the development of new techniques and theoretical insights. The author introduces generalizations for non-smooth objectives and examines convergence through a novel notion of stationarity. By exploring descent conditions and situational convergence, the text broadens traditional analyses and connects diverse minimization strategies.

This book may serve as a basis for students and teachers. The text should provide the reader with a quick overview of the basics for Optimal Control and the link with some important conceptes of applied mathematical, where an agent controls underlying dynamics to find the strategy optimizing some quantity. There are broad applications for optimal control across the natural and social sciences, and the finale to this text is an invitation to read current research on one such application. The balance of the text will prepare the reader to gain a solid understanding of the current research they read.