Adam B. Levy's Books

Attraction in Numerical Minimization

Iteration Mappings, Attractors, and Basins of Attraction

By: Adam B. Levy

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Attraction in Numerical Minimization

Iteration Mappings, Attractors, and Basins of Attraction

By: Adam B. Levy

Numerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are extended to define and explore notions of continuity and differentiability of multiset-mappings, and prove a fixed-point theorem for iteration mappings. Concepts from dynamical systems are utilized to develop notions of basin size and basin entropy. Simulations to estimate basins of attraction, to measure and classify basin size, and to compute basin are included to shed new light on convergence behavior in numerical minimization. Graduate students, researchers, and practitioners in optimization and mathematics who work theoretically to develop solution algorithms will find this book a useful resource.

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Springer

Published Date

ISBN 10

3030040496

ISBN 13

9783030040499

Optimal Control

From Variations to Nanosatellites

By: Adam B. Levy

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Optimal Control

From Variations to Nanosatellites

By: Adam B. Levy

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.

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176

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3111290158

ISBN 13

9783111290157

The Basics of Practical Optimization

By: Adam B. Levy

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The Basics of Practical Optimization

By: Adam B. Levy

Introduces undergraduate students to optimization and its applications using relevant and realistic problems.

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157

Publisher

SIAM

Published Date

ISBN 10

0898716799

ISBN 13

9780898716795

Stationarity and Convergence in Reduce-or-Retreat Minimization

By: Adam B. Levy

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Stationarity and Convergence in Reduce-or-Retreat Minimization

By: Adam B. Levy

Stationarity and Convergence in Reduce-or-Retreat Minimization presents and analyzes a unifying framework for a wide variety of numerical methods in optimization. The author’s “reduce-or-retreat” framework is a conceptual method-outline that covers any method whose iterations choose between reducing the objective in some way at a trial point, or retreating to a closer set of trial points. The alignment of various derivative-based methods within the same framework encourages the construction of new methods, and inspires new theoretical developments as companions to results from across traditional divides. The text illustrates the former by developing two generalizations of classic derivative-based methods which accommodate non-smooth objectives, and the latter by analyzing these two methods in detail along with a pattern-search method and the famous Nelder-Mead method.In addition to providing a bridge for theory through the “reduce-or-retreat” framework, this monograph extends and broadens the traditional convergence analyses in several ways. Levy develops a generalized notion of approaching stationarity which applies to non-smooth objectives, and explores the roles of the descent and non-degeneracy conditions in establishing this property. The traditional analysis is broadened by considering “situational” convergence of different elements computed at each iteration of a reduce-or-retreat method. The “reduce-or-retreat” framework described in this text covers specialized minimization methods, some general methods for minimization and a direct search method, while providing convergence analysis which complements and expands existing results.

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Springer Science & Business Media

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1461446422

ISBN 13

9781461446422

Book's by Adam B. Levy

Attraction in Numerical Minimization

Attraction in Numerical Minimization

Optimal Control

Optimal Control

The Basics of Practical Optimization

The Basics of Practical Optimization

Stationarity and Convergence in Reduce-or-Retreat Minimization

Stationarity and Convergence in Reduce-or-Retreat Minimization

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