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Introduction to linear optimization (Record no. 2944)

000 -LEADER
fixed length control field 05992 a2200277 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20250709114917.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 250709b ||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
ISBN 9781886529199
041 ## - LANGUAGE CODE
Language code of text/sound track or separate title eng
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 519.72 BER/I
100 ## - MAIN ENTRY--AUTHOR NAME
Personal name Bertimas, Dimitris
100 ## - MAIN ENTRY--AUTHOR NAME
Personal name Tsitsiklis, John N.
245 ## - TITLE STATEMENT
Title Introduction to linear optimization
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher Athena Scientific
Year of publication 1997
Place of publication New Hampshire
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher Dynamic Ideas
Year of publication 1997
Place of publication Massachusetts
300 ## - PHYSICAL DESCRIPTION
Number of Pages xv, 587p.; 24cm.
500 ## - GENERAL NOTE
General note <br/>Table of Contents:<br/><br/> 1. Introduction<br/> 1. Variants of the linear programming problem<br/> 2. Examples of linear programming problems<br/> 3. Piecewise linear convex objective functions<br/> 4. Graphical representation and solution<br/> 5. Linear algebra background and notation<br/> 6. Algorithms and operation counts<br/> 7. Exercises<br/> 8. History, notes, notes and sources<br/> <br/> 2. The geometry of linear programming<br/> 1. Polyhedra and convex sets<br/> 2. Extreme points, vertices, and basic feasible solutions<br/> 3. Polyhedra in standard form<br/> 4. Degeneracy<br/> 5. Existence of extreme points<br/> 6. Optimality of extreme points<br/> 7. Representation of bounded polyhedra<br/> 8. Projections of polyhedra: Fourier-Motzkin elimination<br/> 9. Summary<br/> 10. Exercises<br/> 11. Notes and sources<br/> <br/> 3. The simplex method<br/> 1. Optimality conditions<br/> 2. Development of the simplex method<br/> 3. Implementations of the simplex method<br/> 4. Anticycling: lexicography and Bland's rule<br/> 5. Finding an initial basic feasible solution<br/> 6. Column geometry and the simplex method<br/> 7. Computational efficiency of the simplex method<br/> 8. Summary<br/> 9. Exercises<br/> 10. Notes and sources<br/> <br/> 4. Duality theory<br/> 1. Motivation<br/> 2. The dual problem<br/> 3. The duality theorem<br/> 4. Optimal dual variables as marginal costs<br/> 5. Standard form problems and the dual simplex method<br/> 6. Farkas' lemma and linear inequalities<br/> 7. From separating hyperplanes to duality<br/> 8. Cones and extreme rays<br/> 9. Representation of polyhedra<br/> 10. General linear programming duality<br/> 11. Summary<br/> 12. Exercises<br/> 13. Notes and sources<br/> <br/> 5. Sensitivity analysis<br/> 1. Local sensitivity analysis<br/> 2. Global dependence on the right-hand side vector<br/> 3. The set of all dual optimal solutions<br/> 4. Global dependence on the cost vector<br/> 5. Parametric programming<br/> 6. Summary<br/> 7. Exercises<br/> 8. Notes and sources<br/> <br/> 6. Large scale optimization<br/> 1. Delayed column generation<br/> 2. The cutting stock problem<br/> 3. Cutting plane methods<br/> 4. Dantzig-Wolfe decomposition<br/> 5. Stochastic programming and Benders decomposition<br/> 6. Summary<br/> 7. Exercises<br/> 8. Notes and sources<br/> <br/> 7. Network flow problems<br/> 1. Graphs<br/> 2. Formulation of the network flow problem<br/> 3. The network simplex algorithm<br/> 4. The negative cost cycle algorithm<br/> 5. The maximum flow problem<br/> 6. Duality in network flow problems<br/> 7. Dual ascent methods<br/> 8. The assignment problem and the auction algorithm<br/> 9. The shortest path problem<br/> 10. The minimum spanning tree problem<br/> 11. Summary<br/> 12. Exercises<br/> 13. Notes and sources<br/> <br/> 8. Complexity of linear programming and the ellipsoid method<br/> 1. Efficient algorithms and computational complexity<br/> 2. The key geometric result behind the ellipsoid method<br/> 3. The ellipsoid method for the feasibility problem<br/> 4. The ellipsoid method for optimization<br/> 5. Problems with exponentially many constraints<br/> 6. Summary<br/> 7. Exercises<br/> 8. Notes and sources<br/> <br/> 9. Interior point methods<br/> 1. The affine scaling algorithm<br/> 2. Convergence of affine scaling<br/> 3. The potential reduction algorithm<br/> 4. The primal path following algorithm<br/> 5. The primal-dual path following algorithm<br/> 6. An overview<br/> 7. Exercises<br/> 8. Notes and sources<br/> <br/> 10. Integer programming formulations<br/> 1. Modeling techniques<br/> 2. Guidelines for strong formulations<br/> 3. Modeling with exponentially many constraints<br/> 4. Summary<br/> 5. Exercises<br/> 6. Notes and sources<br/> <br/> 11. Integer programming methods<br/> 1. Cutting plane methods<br/> 2. Branch and bound<br/> 3. Dynamic programming<br/> 4. Integer programming duality<br/> 5. Approximation algorithms<br/> 6. Local search<br/> 7. Simulated annealing<br/> 8. Summary<br/> 9. Exercises<br/> 10. Notes and sources<br/> <br/> 12. The art in linear optimization<br/> 1. Modeling languages for linear optimization<br/> 2. Optimization libraries and general observations<br/> 3. The fleet assignment problem<br/> 4. The air traffic flow management problem<br/> 5. The job shop scheduling problem<br/> 6. Summary<br/> 7. Exercises<br/> 8. Notes and sources<br/> <br/> References<br/> Index<br/><br/>
520 ## - SUMMARY, ETC.
Summary, etc This book provides a unified, insightful, and modern treatment of linear optimization, that is, linear programming, network flow problems, and discrete optimization. It includes classical topics as well as the state of the art, in both theory and practice.<br/><br/>
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Mathematics
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Probabilities and applied mathematics
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Linear programming
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Mathematical optimization
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Computer science
856 ## - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://athenasc.com/linoptbook.html
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Book

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