Maxima and Minima with Applications: Practical Optimization and DualityJohn Wiley & Sons, 6 Kas 1998 - 296 sayfa This new work by Wilfred Kaplan, the distinguished author of influential mathematics and engineering texts, is destined to become a classic. Timely, concise, and content-driven, it provides an intermediate-level treatment of maxima, minima, and optimization. Assuming only a background in calculus and some linear algebra, Professor Kaplan presents topics in order of difficulty. In four short chapters, he describes basic concepts and geometric aspects of maxima and minima, progresses to problems with side conditions, introduces optimization and programming, and concludes with an in-depth discussion of research topics involving the duality theorems of Fenchel and Rockafellar. Throughout the text, the subject of convexity is gradually developed-from its theoretical underpinnings to problems, and finally, to its role in applications. Other features include: * A strong emphasis on practical applications of maxima and minima * An impressive array of supporting topics such as numerical analysis * An ample number of examples and problems * More than 60 illustrations highlighting the text * Algorithms to reinforce concepts * An appendix reviewing the prerequisite linear algebra Maxima and Minima with Applications is an ideal text for upper-undergraduate and graduate students taking courses in operations research, management, general engineering, and applied mathematics. It can also be used to supplement courses on linear and nonlinear optimization. This volume's broad scope makes it an excellent reference for professionals wishing to learn more about cutting-edge topics in optimization and mathematical programming. |
İçindekiler
561 | 49 |
Side Conditions | 85 |
Optimization | 135 |
FenchelRockafellar Duality Theory | 203 |
Linear Algebra | 263 |
| 279 | |
| 280 | |
Diğer baskılar - Tümünü görüntüle
Maxima and Minima with Applications: Practical Optimization and Duality Wilfred Kaplan Sınırlı önizleme - 2011 |
Sık kullanılan terimler ve kelime öbekleri
active at xo algorithm apply assume b₁ bounded closed set column concave function consider constant convex function convex set coordinates corresponding critical point curve defined differential equations directional derivative distance dual problem duality theorem E₁ eigenvalues Example extreme point Fenchel Fermat-Weber problem function ƒ ƒ is convex given global minimum gradient graph hence Hessian matrix inner product interval invertible Jacobian matrix Karush-Kuhn-Tucker conditions Lagrange multipliers Lemma level set line segment linear equations linear variety linearly independent local minimum mapping maximizer maximum method Minkowski norm neighborhood nonempty nonnegative obtain optimal origin orthogonal p-norm plane point xo positive definite proof quadratic form quadratic function relative boundary point relative interior relative interior point rule satisfied Section 3.1 Show side conditions strictly convex sublevel set subspace supporting hyperplane surface surplus variables tangent verify Witzgall x₁ xy-plane y₁