Nonlinear Programming Theory and Algorithms 3rd Edition by Mokhtar Bazaraa, Hanif Sherali, Shetty ISBN 1118626303 9781118626306

Nonlinear Programming: Theory and Algorithms 3rd Edition by Mokhtar S. Bazaraa, Hanif D. Sherali, C. M. Shetty – Ebook PDF Instant Download/Delivery: 1118626303, 978-1118626306

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Product details:

ISBN 10: 1118626303

ISBN 13: 978-1118626306

Author:  Mokhtar S. Bazaraa, Hanif D. Sherali, C. M. Shetty 

Nonlinear Programming: Theory and Algorithms 3rd Edition: Presents recent developments of key topics in nonlinear programming using a logical and self-contained format. Divided into three sections that deal with convex analysis, optimality conditions and duality, computational techniques. Precise statements of algorithms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations and numerous exercises to aid readers in understanding the concepts and methods discussed.

 

Nonlinear Programming: Theory and Algorithms 3rd Edition Table of contents:

Chapter 1: Introduction

• 1.1 Problem Statement and Basic Definitions
• 1.2 Illustrative Examples
• 1.3 Guidelines for Model Construction
• Exercises
• Notes and References

Part 1: Convex Analysis

Chapter 2: Convex Sets

• 2.1 Convex Hulls
• 2.2 Closure and Interior of a Set
• 2.3 Weierstrass’s Theorem
• 2.4 Separation and Support of Sets
• 2.5 Convex Cones and Polarity
• 2.6 Polyhedral Sets, Extreme Points, and Extreme Directions
• 2.7 Linear Programming and the Simplex Method
• Exercises
• Notes and References

Chapter 3: Convex Functions and Generalizations

• 3.1 Definitions and Basic Properties
• 3.2 Subgradients of Convex Functions
• 3.3 Differentiable Convex Functions
• 3.4 Minima and Maxima of Convex Functions
• 3.5 Generalizations of Convex Functions
• Exercises
• Notes and References

Part 2: Optimality Conditions and Duality

Chapter 4: Fritz John and Karush–Kuhn–Tucker (KKT) Conditions

• 4.1 Unconstrained Problems
• 4.2 Inequality-Constrained Problems
• 4.3 Problems with Both Inequality and Equality Constraints
• 4.4 Second-Order Optimality Conditions
• Exercises
• Notes and References

Chapter 5: Constraint Qualifications

• 5.1 Cone of Tangents
• 5.2 Other Constraint Qualifications
• 5.3 Mixed Constraints (Inequality & Equality)
• Exercises
• Notes and References

Chapter 6: Lagrangian Duality and Saddle Point Conditions

• 6.1 Lagrangian Dual Problem
• 6.2 Duality Theorems and Saddle Point Conditions
• 6.3 Properties of the Dual Function
• 6.4 Solving the Dual Problem
• 6.5 Deriving the Primal Solution
• 6.6 Linear and Quadratic Programs
• Exercises
• Notes and References

Part 3: Algorithms and Their Convergence

Chapter 7: The Concept of an Algorithm

• 7.1 Algorithms and Algorithmic Maps
• 7.2 Closed Maps and Convergence
• 7.3 Composition of Mappings
• 7.4 Comparing Algorithms
• Exercises
• Notes and References

Chapter 8: Unconstrained Optimization

• 8.1 Line Search (Without Derivatives)
• 8.2 Line Search (With Derivatives)
• 8.3 Practical Line Search Methods
• 8.4 Multidimensional Search (With/Without Derivatives)
• 8.5 Newton’s Method, Levenberg-Marquardt, Trust Region Methods
• 8.6 Conjugate Directions: Quasi-Newton, Conjugate Gradient Methods
• 8.7 Subgradient Optimization
• Exercises
• Notes and References

Chapter 9: Penalty and Barrier Functions

• 9.1 Penalty Function Concepts
• 9.2 Exterior Penalty Methods
• 9.3 Augmented Lagrangian Methods
• 9.4 Barrier Function Methods
• 9.5 Interior Point Algorithms for Linear Programming
• Exercises
• Notes and References

Chapter 10: Methods of Feasible Directions

• 10.1 Zoutendijk’s Method
• 10.2 Successive Linear Programming
• 10.3 Successive Quadratic Programming
• 10.4 Gradient Projection Method
• 10.5 Reduced Gradient and Convex-Simplex Methods
• Exercises
• Notes and References

Chapter 11: Specialized Programming Problems

• 11.1 Linear Complementary Problem
• 11.2 Convex/Nonconvex Quadratic Programming
• 11.3 Separable Programming
• 11.4 Linear Fractional Programming
• 11.5 Geometric Programming
• Exercises
• Notes and References

 

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