M. Asghar Bhatti

Practical Optimization Methods (eBook, PDF)

With Mathematica® Applications

• Format: PDF

Produktbeschreibung

This book is suitable for practicing scientists and engineers especially those using mathematica in their work.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 715
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461205012
• Artikelnr.: 44185269

Inhaltsangabe

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.