Variational Calculus And Optimal Control

This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines and in particular from Economics and Social Sciences. The first part develops the fundamental aspects of mathematical modeling, dealing with both continuous time systems (differential equations) and discrete time systems (difference equations). Particular attention is devoted to equilibria, their classification in the linear case, and their stability.

This publication is a Special Issue of the journal Axioms entitled “Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th birthday”. This Special Issue is dedicated to Professor Delfim F. M. Torres on his 50th birthday, as a recognition of his significant contributions to Mathematics, in particular regarding the calculus of variations, optimal control, and mathematical biology. Professor Torres is a distinguished University Professor, a highly cited researcher in Mathematics (in the top 1% for Mathematics in the Web of Science in 2015, 2016, 2017, and 2019), and a lifetime member of the American Mathematical Society.

Authors: Locatelli, Arturo
Presents the basic issues of Pontryagin’s maximum principle in a reader-friendly yet rigorous way
Discusses in detail a broad range of problems, allowing readers to readily grasp all aspects of the topic considered
Explores the maximum principle in the presence of both simple and complex constraints

by Alexander Zaslavski (Author)

This undergraduate textbook introduces students of science and engineering to the fascinating field of optimization. It is a unique book that brings together the subfields of mathematical programming, variational calculus, and optimal control, thus giving students an overall view of all aspects of optimization in a single reference. As a primer on optimization, its main goal is to provide a succinct and accessible introduction to linear programming, nonlinear programming, numerical optimization algorithms, variational problems, dynamic programming, and optimal control. Prerequisites have been kept to a minimum, although a basic knowledge of calculus, linear algebra, and differential equations is assumed. There are numerous examples, illustrations, and exercises throughout the text, making it an ideal book for self-study. Applied mathematicians, physicists, engineers, and scientists will all find this introduction to optimization extremely useful.