Read more
Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line. Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations are illustrated throughout this book. This book also contains significant results and information about the turnpike property of the variational problems. This well-known property is a general phenomenon which holds for large classes of variational problems. The author examines the following in relation to the turnpike property in individual (non-generic) turnpike results, sufficient and necessary conditions for the turnpike phenomenon as well as in the non-intersection property for extremals of variational problems. This book appeals to mathematicians working in optimal control and the calculus as well as with graduate students.
List of contents
Preface.- 1. Introduction.- 2. Nonautonomous problems.- 3.Autonomous problems.- 4.Convex Autonomous Problems.- References.- Index.
About the author
Alexander J. Zaslavski, is a senior researcher at the Technion - Israel Institute of Technology. He was born in Ukraine in 1957 and got his PhD in Mathematical Analysis in 1983, The Institute of Mathematics, Novosibirsk. He is the author of 26 research monographs and more than 600 research papers and editor of more than 70 edited volumes and journal special issues. He is the Founding Editor and Editor-in Chief of the journal Pure and Applied Functional Analysis, and Editor-in-Chief of journal Communications in Optimization Theory. His area of research contains nonlinear functional analysis, control theory, optimization, calculus of variations, dynamical systems theory, game theory and mathematical economics.
Summary
Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line. Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations are illustrated throughout this book. This book also contains significant results and information about the turnpike property of the variational problems. This well-known property is a general phenomenon which holds for large classes of variational problems. The author examines the following in relation to the turnpike property in individual (non-generic) turnpike results, sufficient and necessary conditions for the turnpike phenomenon as well as in the non-intersection property for extremals of variational problems. This book appeals to mathematicians working in optimal control and the calculus as well as with graduate students.
Additional text
From the reviews:
“The book contains the most recent collection of various concepts, significant results and techniques about the turnpike property, which is a phenomenon that occurs for large classes of variational problems. … The book is supplemented by an almost exhaustive bibliography. It would probably be useful to give more applications of the results to specific problems to make the subject and the questions more appealing to non-expert researchers in the field and graduate students.” (Elvira Mascolo, zbMATH, Vol. 1272, 2013)
Report
From the reviews:
"The book contains the most recent collection of various concepts, significant results and techniques about the turnpike property, which is a phenomenon that occurs for large classes of variational problems. ... The book is supplemented by an almost exhaustive bibliography. It would probably be useful to give more applications of the results to specific problems to make the subject and the questions more appealing to non-expert researchers in the field and graduate students." (Elvira Mascolo, zbMATH, Vol. 1272, 2013)
