Infinite-Dimensional Optimization and Convexity

Ivar Ekeland and Thomas Turnbull

Infinite-Dimensional Optimization and Convexity
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Ivar Ekeland and Thomas Turnbull

174 pages | 5-1/4 x 8 | © 1983
Paper $30.00 ISBN: 9780226199887 Published September 1983
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.
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
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