عنوان

Linear and nonlinear programming /

شابک

3319188410

شابک

3319188429

شابک

9783319188416

شابک

9783319188423

شابک اشتباه

9783319188423

شماره

dltt

عنوان اصلي

Linear and nonlinear programming /

نام عام مواد

[Book]

نام نخستين پديدآور

David G. Luenberger, Yinyu Ye.

وضعيت ويراست

Fourth edition.

نام خاص و کميت اثر

xiii, 546 pages :

ساير جزييات

illustrations (black and white) ;

ابعاد

25 cm.

عنوان فروست

International series in operations research & management science,

مشخصه جلد

volume 228.

شاپا ي ISSN فروست

0884-8289 ;

متن يادداشت

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

متن يادداشت

Includes bibliographical references and index.

متن يادداشت

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.

متن يادداشت

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.

متن يادداشت

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.

متن يادداشت

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.

متن يادداشت

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.

متن يادداشت

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.

بدون عنوان

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عنوان

International Series in Operations Research & Management Science ; 228

موضوع مستند نشده

Linear programming.

موضوع مستند نشده

Nonlinear programming.

موضوع مستند نشده

Business.

موضوع مستند نشده

Decision making.

موضوع مستند نشده

Engineering economics.

موضوع مستند نشده

Engineering economy.

موضوع مستند نشده

Management science.

موضوع مستند نشده

Mathematical models.

موضوع مستند نشده

Nonlinear programming, Mathematical optimization.

موضوع مستند نشده

Operations research.

موضوع مستند نشده

Programmation non linéaire, Optimisation mathématique.

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Luenberger, David G.,1937-

مستند نام اشخاص تاييد نشده

Ye, Yinyu

تاريخ عمليات

20170908104232.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y