Infinite-Dimensional Optimization and Convexity

by Ivar Ekeland, Thomas Turnbull

Overview

In this volume, Ekeland and Turnbull are mainly concerned with existence theory. They seek to determine whether, when given an optimization problem consisting of minimizing a functional over some feasible set, an optimal solution—a minimizer—may be found.

Product Details

ISBN-13:	9780226199887
Publisher:	University of Chicago Press
Publication date:	09/15/1983
Series:	Chicago Lectures in Mathematics
Pages:	174
Product dimensions:	5.25(w) x 8.00(h) x 0.60(d)

About the Author

Ivar Ekeland is professor of mathematics at the University of Paris-Dauphine. Thomas Turnbull is a student in the Graduate School of Business at the University of Chicago.

Table of Contents

Foreword
Chapter I - The Caratheodory Approach
1. Optimal Control Problems
2. Hamiltonian Systems
Chapter II - Infinite-dimensional Optimization
1.  The Variational Principle
2.  Strongly Continuous Functions on LP-spaces
3. Smooth Optimization in L2
4. Weak Topologies
5. Existence Theory for the Calculus of Variations
Chapter III - Duality Theory
1. Convex Analysis
2. Subdifferentiability
3.  Necessary Conditions and Duality Theory
4. Non-convex Duality Theory
5. Applications of Duality to the Calculus of Variations
6.  Relaxation  Theory
Notes
References