The German edition of this book, first published in 1966, has been quite popular; we did not, however, consider publishing an English edition because a number of excellent textbooks in this field already exist. In recent years, howยญ ever, the wish was frequently expressed that, especially, the description of the relationships between optimization and other subfields of mathematics, which is not to be found in this form in other texts, might be made available to a wider readership; so it was with this in mind that, beยญ latedly, a translation was undertaken after all. Since the appearance of the German edition, the field of optimization has continued to develop at an unabated rate. A completely current presentation would have required a total reworking of the book; unfortunately, this was not possible. For example, we had to ignore the extensive progress which has been made in the development of numerical methods which do not require convexity assumptions to find local maxima and minima of non-linear optimization problems. These methods are also applicable to boundary value, and other, problems. Many new results, both of a numerical and a theoretical naยญ ture, which are especially relevant to applications, are to be found in the areas of optimal contol and integer optimizaยญ tion
CONTENT
I. Linear Optimization -- ยง1. Introduction -- ยง2. Linear Optimization and Polyhedra -- ยง3. Vertex Exchange and the Simplex Method -- ยง4. Algorithmic Implementation of the Simplex Method -- ยง5. Dual Linear Optimization Problems -- II. Convex Optimization -- ยง6. Introduction -- ยง7. A Characterization of Minimal Solutions for Convex Optimization -- ยง8. Convex Optimization for Differentiable Functions -- ยง9. Convex Optimization with Affine Linear Constraints -- ยง10. The Numerical Treatment of Convex Optimization Problems -- III. Quadratic Optimization -- ยง11. Introduction -- ยง12. The Kuhn-Tucker Theorem and Applications. -- ยง13. Duality for Quadratic Optimization -- ยง14. The Numerical Treatment of Quadratic Optimization Problems -- IV. Tchebychev Approximation and Optimization -- ยง 15. Introduction -- ยง16. Discrete Linear Tchebychev Approximation -- ยง17. Further Types of Approximation Problems -- V. Elements of Game Theory -- ยง18. Matrix Games (Two Person Zero Sum Games) -- ยง19. n-Person Games -- Problems
