عنوان

Linear and nonlinear programming /

(Number (ISBN

3319188410

(Number (ISBN

3319188429

(Number (ISBN

9783319188416

(Number (ISBN

9783319188423

Erroneous ISBN

9783319188423

Number

dltt

Title Proper

Linear and nonlinear programming /

General Material Designation

[Book]

First Statement of Responsibility

David G. Luenberger, Yinyu Ye.

Edition Statement

Fourth edition.

Specific Material Designation and Extent of Item

xiii, 546 pages :

Other Physical Details

illustrations (black and white) ;

Dimensions

25 cm.

Series Title

International series in operations research & management science,

Volume Designation

volume 228.

ISSN of Series

0884-8289 ;

Text of Note

"ISSN 2214-7934 (electronic)"--Title page verso.

Text of Note

Includes bibliographical references and index.

Text of Note

Machine generated contents note: 1. Introduction -- 1.1. Optimization -- 1.2. Types of Problems -- 1.3. Size of Problems -- 1.4. Iterative Algorithms and Convergence -- pt. I Linear Programming -- 2. Basic Properties of Linear Programs -- 2.1. Introduction -- 2.2. Examples of Linear Programming Problems -- 2.3. Basic Solutions -- 2.4. The Fundamental Theorem of Linear Programming -- 2.5. Relations to Convexity -- 2.6. Exercises -- 3. The Simplex Method -- 3.1. Pivots -- 3.2. Adjacent Extreme Points -- 3.3. Determining a Minimum Feasible Solution -- 3.4.Computational Procedure: Simplex Method -- 3.5. Finding a Basic Feasible Solution -- 3.6. Matrix Form of the Simplex Method -- 3.7. Simplex Method for Transportation Problems -- 3.8. Decomposition -- 3.9. Summary -- 3.10. Exercises -- 4. Duality and Complementarity -- 4.1. Dual Linear Programs -- 4.2. The Duality Theorem -- 4.3. Relations to the Simplex Procedure -- 4.4. Sensitivity and Complementary Slackness -- 4.5. Max Flow -- Min Cut Theorem.

Text of Note

Note continued: 10.5. Convergence Properties -- 10.6. Scaling -- 10.7. Memoryless Quasi-Newton Methods -- 10.8.*Combination of Steepest Descent and Newton's Method -- 10.9. Summary -- 10.10. Exercises -- pt. III Constrained Minimization -- 11. Constrained Minimization Conditions -- 11.1. Constraints -- 11.2. Tangent Plane -- 11.3. First-Order Necessary Conditions (Equality Constraints) -- 11.4. Examples -- 11.5. Second-Order Conditions -- 11.6. Eigenvalues in Tangent Subspace -- 11.7. Sensitivity -- 11.8. Inequality Constraints -- 11.9. Zero-Order Conditions and Lagrangian Relaxation -- 11.10. Summary -- 11.11. Exercises -- 12. Primal Methods -- 12.1. Advantage of Primal Methods -- 12.2. Feasible Direction Methods -- 12.3. Active Set Methods -- 12.4. The Gradient Projection Method -- 12.5. Convergence Rate of the Gradient Projection Method -- 12.6. The Reduced Gradient Method -- 12.7. Convergence Rate of the Reduced Gradient Method -- 12.8.*Variations -- 12.9. Summary -- 12.10. Exercises.

Text of Note

Note continued: 13. Penalty and Barrier Methods -- 13.1. Penalty Methods -- 13.2. Barrier Methods -- 13.3. Properties of Penalty and Barrier Functions -- 13.4. Newton's Method and Penalty Functions -- 13.5. Conjugate Gradients and Penalty Methods -- 13.6. Normalization of Penalty Functions -- 13.7. Penalty Functions and Gradient Projection -- 13.8.*Exact Penalty Functions -- 13.9. Summary -- 13.10. Exercises -- 14. Duality and Dual Methods -- 14.1. Global Duality -- 14.2. Local Duality -- 14.3. Canonical Convergence Rate of Dual Steepest Ascent -- 14.4. Separable Problems and Their Duals -- 14.5. Augmented Lagrangian -- 14.6. The Method of Multipliers -- 14.7. The Alternating Direction Method of Multipliers -- 14.8.̀Cutting Plane Methods -- 14.9. Exercises -- 15. Primal-Dual Methods -- 15.1. The Standard Problem -- 15.2.A Simple Merit Function -- 15.3. Basic Primal-Dual Methods -- 15.4. Modified Newton Methods -- 15.5. Descent Properties -- 15.6.̀Rate of Convergence.

Text of Note

Note continued: 15.7. Primal-Dual Interior Point Methods -- 15.8. Summary -- 15.9. Exercises -- A. Mathematical Review -- A.1. Sets -- A.2. Matrix Notation -- A.3. Spaces -- A.4. Eigenvalues and Quadratic Forms -- A.5. Topological Concepts -- A.6. Functions -- B. Convex Sets -- B.1. Basic Definitions -- B.2. Hyperplanes and Polytopes -- B.3. Separating and Supporting Hyperplanes -- B.4. Extreme Points -- C. Gaussian Elimination -- D. Basic Network Concepts -- D.1. Flows in Networks -- D.2. Tree Procedure -- D.3. Capacitated Networks.

Text of Note

Note continued: 4.6. The Dual Simplex Method -- 4.7.*The Primal-Dual Algorithm -- 4.8. Summary -- 4.9. Exercises -- 5. Interior-Point Methods -- 5.1. Elements of Complexity Theory -- 5.2.*The Simplex Method Is Not Polynomial-Time -- 5.3.*The Ellipsoid Method -- 5.4. The Analytic Center -- 5.5. The Central Path -- 5.6. Solution Strategies -- 5.7. Termination and Initialization -- 5.8. Summary -- 5.9. Exercises -- 6. Conic Linear Programming -- 6.1. Convex Cones -- 6.2. Conic Linear Programming Problem -- 6.3. Farkas' Lemma for Conic Linear Programming -- 6.4. Conic Linear Programming Duality -- 6.5.Complementarity and Solution Rank of SDP -- 6.6. Interior-Point Algorithms for Conic Linear Programming -- 6.7. Summary -- 6.8. Exercises -- pt. II Unconstrained Problems -- 7. Basic Properties of Solutions and Algorithms -- 7.1. First-Order Necessary Conditions -- 7.2. Examples of Unconstrained Problems -- 7.3. Second-Order Conditions -- 7.4. Convex and Concave Functions.

Text of Note

Note continued: 7.5. Minimization and Maximization of Convex Functions -- 7.6.*Zero-Order Conditions -- 7.7. Global Convergence of Descent Algorithms -- 7.8. Speed of Convergence -- 7.9. Summary -- 7.10. Exercises -- 8. Basic Descent Methods -- 8.1. Line Search Algorithms -- 8.2. The Method of Steepest Descent -- 8.3. Applications of the Convergence Theory -- 8.4. Accelerated Steepest Descent -- 8.5. Newton's Method -- 8.6. Coordinate Descent Methods -- 8.7. Summary -- 8.8. Exercises -- 9. Conjugate Direction Methods -- 9.1. Conjugate Directions -- 9.2. Descent Properties of the Conjugate Direction Method -- 9.3. The Conjugate Gradient Method -- 9.4. The C -- G Method as an Optimal Process -- 9.5. The Partial Conjugate Gradient Method -- 9.6. Extension to Nonquadratic Problems -- 9.7.*Parallel Tangents -- 9.8. Exercises -- 10. Quasi-Newton Methods -- 10.1. Modified Newton Method -- 10.2. Construction of the Inverse -- 10.3. Davidon-Fletcher-Powell Method -- 10.4. The Broyden Family.

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Title

International Series in Operations Research & Management Science ; 228

Linear programming.

Nonlinear programming.

Business.

Decision making.

Engineering economics.

Engineering economy.

Management science.

Mathematical models.

Nonlinear programming, Mathematical optimization.

Operations research.

Programmation non linéaire, Optimisation mathématique.

Number

Edition

Class number

Book number

Luenberger, David G.,1937-

Ye, Yinyu

Date of Transaction

20170908104232.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y