Optimization Theory [Paperback]

This volume provides a comprehensive introduction to the theory of (deterministic) optimization. It covers both continuous and discrete optimization. This allows readers to study problems under different points-of-view, which supports a better understanding of the entire field. Many exercises are included to increase the reader's understanding.

Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc.
This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level. One main feature is the treatment of both continuous and discrete optimization at the same place. This allows to study the problems under different points of view, supporting a better understanding of the entire field.
Audience: The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course; however, each of its parts can also be taught separately. Many exercises are included to increase the reader's understanding.Preface.- PART I. CONTINUOUS OPTIMIZATION.- 1. Optimality Criteria on Simple Regions.- 2. Constraints, Lagrange Function, Optimality.- 3. Parametric Aspects, Semi-Infinite Optimization.- 4. Convex Functions, Duality, Separation Theorem.- 5. Linear Inequalities, Constraint Qualifications.- 6. Linear Programming: The Simplex Method.- 7. The Ellipsoid Method.- 8. Karmarkars Method for Linear Programming.- 9. Order of Convergence, Steepest Descent.- 10. Conjugate Direction, Variable Metric.- 11. Penalty-, Barrier-, Multiplier-, IP-Methods.- 12. Search Methods without Derivatives.- 13. One-Dimensional Minimization.- PART II. DISCRETE OPTIMIZATION.- 14. Graphs and Networks.- 15. Flows in Networks.- 16. Applications of the Mlƒ*