Linear and Nonlinear Programming

• Κύριοι συγγραφείς: Luenberger, David G. (Συγγραφέας), Ye, Yinyu (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Έκδοση: 4th ed. 2016.
• Σειρά: International Series in Operations Research & Management Science, 228
• Θέματα: Business.; Operations research.; Decision making.; Mathematical models.; Management science.; Engineering economics.; Engineering economy.; Business and Management.; Operation Research/Decision Theory.; Operations Research, Management Science.; Mathematical Modeling and Industrial Mathematics.; Engineering Economics, Organization, Logistics, Marketing.

 This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular.  Again a connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve the problem.  As in the earlier editions, the material in this fourth edition is organized into three separate parts.  Part I is a self-contained introduction to linear programming covering numerical algorithms and many of its important special applications.  Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms.  Part III extends the concepts developed in the second part to constrained optimization problems.  It is possible to go directly into Parts II and III omitting Part I, and, in fact, the book has been used in this way in many universities.   <New to this edition is a chapter devoted to Conic Linear Programming, a powerful generalization of Linear Programming.  Indeed, many conic structures are possible and useful in a variety of applications.  It must be recognized, however, that conic linear programming is an advanced topic, requiring special study.  Other important and popular topics include (1) an accelerated steepest descent method that exhibits superior convergence properties and (2) the alternating direction method with multipliers (ADMM) that can be implemented distributionally.  The proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8, and the analysis of ADMM in Chapter 14 as a dual method.  As in previous editions, end-of-chapter exercises appear for most chapters.   From the reviews of the Third Edition   “….this very well-written book is a classic textbook in Optimization.  It should be present in the bookcase of each student, researcher, and specialist from the host of disciplines from which practical optimization applications are drawn.”  (Jean-Jacques Strodiot, Zentralblatt  MATH, Vol.1207, 2011). 

 Introduction -- Part I Linear Programming -- Basic Properties of Linear Programs -- The Simplex Method -- Duality and Complementarity -- Interior-Point Methods -- Conic Linear Programming -- Part II Unconstrained Problems -- Basic Properties of Solutions and Algorithms -- Basic Descent Methods -- Conjugate Direction Methods -- Quasi-Newton Methods -- Part III Constrained Minimization -- Constrained Minimization Conditions -- Primal Methods -- Penalty and Barrier Methods -- Duality and Dual Methods -- Primal-Dual Methods -- Appendix A: Mathematical Review -- Appendix B: Convex Sets -- Appendix C: Gaussian Elimination -- Appendix D: Basic Network Concepts.