Infinite-Dimensional Optimization and Convexity
174 pages
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5-1/4 x 8
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© 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.
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
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
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