Practical Optimization Methods

With Mathematica® Applications
2000
ISBN: 978-0-387-98631-9
Verlag: Springer

Buch, Englisch, 715 Seiten, HC runder Rücken kaschiert, Format (B × H): 183 mm x 241 mm, Gewicht: 1434 g

This introductory textbook adopts a practical and intuitive approach, rather than emphasizing mathematical rigor. Computationally oriented books in this area generally present algorithms alone, and expect readers to perform computations by hand, and are often written in traditional computer languages, such as Basic, Fortran or Pascal. This book, on the other hand, is the first text to use Mathematica to develop a thorough understanding of optimization algorithms, fully exploiting Mathematica's symbolic, numerical and graphic capabilities.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Bhatti, M. Asghar

Fachgebiete

• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik

Inhaltsverzeichnis

1 Optimization Problem Formulation.- 1.1 Optimization Problem Formulation.- 1.2 The Standard Form of an Optimization Problem.- 1.3 Solution of Optimization Problems.- 1.4 Time Value of Money.- 1.5 Concluding Remarks.- 1.6 Problems.- 2 Graphical Optimization.- 2.1 Procedure for Graphical Optimization.- 2.2 GraphicalSolution function.- 2.3 Graphical Optimization Examples.- 2.4 Problems.- 3 Mathematical Preliminaries.- 3.1 Vectors and Matrices.- 3.2 Approximation Using the Taylor Series.- 3.3 Solution of Nonlinear Equations.- 3.4 Quadratic Forms.- 3.5 Convex Functions and Convex Optimization Problems.- 3.6 Problems.- 4 Optimality Conditions.- 4.1 Optimality Conditions for Unconstrained Problems.- 4.2 The Additive Property of Constraints.- 4.3 Karush-Kuhn-Tucker (KT) Conditions.- 4.4 Geometric Interpretation of KT Conditions.- 4.5 Sensitivity Analysis.- 4.6 Optimality Conditions for Convex Problems.- 4.7 Second-Order Sufficient Conditions.- 4.8 Lagrangian Duality.- 4.9 Problems.- 5 Unconstrained Problems.- 5.1 Descent direction.- 5.2 Line Search Techniques—Step Length Calculations.- 5.3 Unconstrained Minimization Techniques.- 5.4 Concluding Remarks.- 5.5 Problems.- 6 Linear Programming.- 6.1 The Standard LP Problem.- 6.2 Solving a Linear System of Equations.- 6.3 Basic Solutions of an LP Problem.- 6.4 The Simplex Method.- 6.5 Unusual Situations Arising During the Simplex Solution.- 6.6 Post-Optimality Analysis.- 6.7 The Revised Simplex Method.- 6.8 Sensitivity Analysis Using the Revised Simplex Method.- 6.9 Concluding Remarks.- 6.10 Problems.- 7 Interior Point Methods.- 7.1 Optimality Conditions for Standard LP.- 7.2 The Primal Affine Scaling Method.- 7.3 The Primal-Dual Interior Point Method.- 7.4 Concluding Remarks.- 7.5 Appendix—Null and Range Spaces.- 7.6 Problems.- 8 Quadratic Programming.- 8.1 KT Conditions for Standard QP.- 8.2 The Primal Affine Scaling Method for Convex QP.- 8.3 The Primal-Dual Method for Convex QP.- 8.4 Active Set Method.- 8.5 Active Set Method for the Dual QP Problem.- 8.6 Appendix—Derivation of the Descent Direction Formula for the PAS Method.- 8.7 Problems.- 9 Constrained Nonlinear Problems.- 9.1 Normalization.- 9.2 Penalty Methods.- 9.3 Linearization of a Nonlinear Problem.- 9.4 Sequential Linear Programming—SLP.- 9.5 Basic Sequential Quadratic Programming—SQP.- 9.6 Refined SQP Methods.- 9.7 Problems.- A.1 Basic Manipulations in Mathematica.- A.2 Lists and Matrices.- A.3 Solving Equations.- A.7 Online Help.