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Nonlinear programming: theory and algorithms

Author: Bazaraa, M. S. ; Sherali, Hanif D. ; Shetty, C. M.Publisher: Wiley, 2006.Edition: 3rd ed.Language: EnglishDescription: 853 p. ; 24 cm.ISBN: 9780471486008Type of document: Book Online Access: Click here Note: Doriot: for 2012-2013 coursesBibliography/Index: Includes bibliographical references and index
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Book Asia Campus
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Print T57.8 .B39 2006
(Browse shelf)
900203761
Available 900203761
Book Asia Campus
Textbook Collection (PhD)
Print T57.8 .B39 2006
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900203759
Consultation only 900203759
Book Asia Campus
Textbook Collection (PhD)
Print T57.8 .B39 2006
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900203773
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Book Europe Campus
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Print T57.8 .B39 2006
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001275025
Available For PhD courses 2012/2013 001275025
Book Europe Campus
Main Collection
Print T57.8 .B39 2006
(Browse shelf)
001275063
Available For PhD courses 2012/2013 001275063
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Doriot: for 2012-2013 courses

Includes bibliographical references and index

Digitized

Nonlinear Programming Theory and Algorithms Contents Chapter 1 Introduction 1 1.1 Problem Statement and Basic Definitions 2 1.2 Illustrative Examples 4 1.3 Guidelines for Model Construction 26 Exercises 30 Notes and References 34 Part 1 Convex Analysis 37 Chapter 2 Convex Sets 39 2.1 Convex Hulls 40 2.2 Closure and Interior of a Set 45 2.3 Weierstrass's Theorem 48 2.4 Separation and Support of Sets 50 2.5 Convex Cones and Polarity 62 2.6 Polyhedral Sets, Extreme Points, and Extreme Directions 64 2.7 Linear Programming and the Simplex Method 75 Exercises 86 Notes and References 93 Chapter 3 Convex Functions and Generalizations 97 3.1 3.2 3.3 3.4 3.5 Definitions and Basic Properties 98 Subgradients of Convex Functions 103 Differentiable Convex Functions 109 Minima and Maxima of Convex Functions 123 Generalizations of Convex Functions 134 Exercises 147 Notes and References 159 Part 2 Optimality Conditions and Duality 163 Chapter 4 The Fritz John and Karush--Kuhn--Tucker Optimality Conditions 165 4.1 4.2 4.3 4.4 Unconstrained Problems 166 Problems Having Inequality Constraints 174 Problems Having lnequality and Equality Constraints 197 Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems 211 Exercises 220 Notes and References 235 Chapter 5 Constraint Qualifications 237 5.1 Cone of Tangents 237 5.2 Other Constraint Qualifications 241 5.3 Problems Having Inequality and Equality Constraints 245 Exercises 250 Notes and References 256 Chapter 6 Lagrangian Duality and Saddle Point Optimality Conditions 257 6.1 6.2 6.3 6.4 6.5 6.6 Lagrangian Dual Problem 258 Duality Theorems and Saddle Point Optimality Conditions 263 Properties of the Dual Function 276 Formulating and Solving the Dual Problem 286 Getting the Primal Solution 293 Linear and Quadratic Programs 298 Exercises 300 Notes and References 313 Part 3 Algorithms and Their Convergence 315 Chapter 7 The Concept of an Algorithm 317 7.1 Algorithms and Algorithmic Maps 317 7.2 Closed Maps and Convergence 319 7.3 Composition of Mappings 324 7.4 Comparison Among Algorithms 329 Exercises 332 Notes and References 340 Chapter 8 Unconstrained Optimization 343 8.1 Line Search Without Using Derivatives 344 8.2 Line Search Using Derivatives 356 8.3 Some Practical Line Search Methods 360 8.4 Closedness of the Line Search Algorithmic Map 363 8.5 Multidimensional Search Without Using Derivatives 365 8.6 Multidimensional Search Using Derivatives 384 8.7 Modification of Newton's Method: Levenberg­Marquardt and Trust Region Methods 398 8.8 Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods 402 8.9 Subgradient Optimization Methods 435 Exercises 444 Notes and References 462 Chapter 9 Penalty and Barrier Functions 469 9.1 Concept of Penalty Functions 470 9.2 Exterior Penalty Function Methods 475 9.3 Exact Absolute Value and Augmented Lagrangian Penalty Methods 485 9.4 Barrier Function Methods 501 9.5 Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function 509 Exercises 520 Notes and References 533 Chapter 10 Methods of Feasible Directions 537 10.1 Method of Zoutendijk 538 10.2 Convergence Analysis of the Method of Zoutendijk 557 10.3 Successive Linear Programming Approach 568 10.4 Successive Quadratic Programming or Projected Lagrangian Approach 576 10.5 Gradient Projection Method of Rosen 589 10.6 Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method 602 10.7 Convex--Simplex Method of Zangwill 613 10.8 Effective First- and Second-Order Variants of the Reduced Gradient Method 620 Exercises 625 Notes and References 649 Chapter 11 Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming 655 11.1 Linear Complementary Problem 656 11.2 Convex and Nonconvex Quadratic Programming: Global Optimization Approaches 667 11.3 Separable Programming 684 11.4 Linear Fractional Programming 703 11.5 Geometric Programming 712 Exercises 722 Notes and References 745 Appendix A Mathematical Review 751 Appendix B Summary of Convexity, Optimality Conditions, and Duality 765 Bibliography 779 Index 843

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