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Conjugate Duality and Optimization

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This monograph provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. Emphasizes the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.

Author(s): R. Tyrrell Rockafellar
Series: CBMS-NSF Regional Conference Series in Applied Mathematics
Edition: SIAM
Publisher: Society for Industrial Mathematics
Year: 1987

Language: English
Pages: 85
Tags: Математика;Методы оптимизации;

Conjugate Duality and Optimization......Page 2
CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS......Page 3
ISBN 0-89871-013-8......Page 7
Contents......Page 8
Preface......Page 10
1. The role of convexity and duality......Page 12
2. Examples of convex optimization problems......Page 17
3. Conjugate convex functions in paired spaces......Page 24
4. Dual problems and Lagrangians......Page 29
5. Examples of duality schemes......Page 34
6. Continuity and derivatives of convex functions......Page 41
7. Solutions to optimization problems......Page 49
8. Some applications......Page 56
9. Calculating conjugates and subgradients; integral functionals......Page 63
10. More applications......Page 75
References......Page 84