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Nonlinear Programming Theory and Algorithms

ISBN-10: 0471557935

ISBN-13: 9780471557937

Edition: 2nd 1993 (Revised)

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

List price: $118.95
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Description:

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.
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Book details

List price: $118.95
Edition: 2nd
Copyright year: 1993
Publisher: John Wiley & Sons, Incorporated
Publication date: 1/18/1993
Binding: Paperback
Pages: 656
Size: 7.50" wide x 10.50" long x 1.50" tall
Weight: 3.212
Language: English

Introduction.
Problem Statement and Basic Definitions
Illustrative Examples
Guidelines for Model Construction
Exercises
Notes and References
Convex Analysis.
Convex Sets.
Convex Hulls
Closure and Interior of a Set
Weierstrass's Theorem
Separation and Support of Sets
Convex Cones and Polarity
Polyhedral Sets, Extreme Points, and Extreme Directions
Linear Programming and the Simplex Method
Exercises
Notes and References
Convex Functions and Generalizations.
Definitions and Basic Properties
Subgradients of Convex Functions
Differentiable Convex Functions
Minima and Maxima of Convex Functions
Generalizations of Convex Functions
Exercises
Notes and References
Optimality Conditions and Duality.
The Fritz John and Karush-Kuhn-Tucker Optimality Conditions.
Unconstrained Problems
Problems Having Inequality Constraints
Problems Having Inequality and Equality Constraints
Second-Order Necessary and Sufficient Optimality Conditions for Constrained Problems
Exercises
Notes and References
Constraint Qualifications.
Cone of Tangents
Other Constraint Qualifications
Problems Having Inequality and Equality Constraints
Exercises
Notes and References
Lagrangian Duality and Saddle Point Optimality Conditions.
Lagrangian Dual Problem
Duality Theorems and Saddle Point Optimality Conditions
Properties of the Dual Function
Formulating and Solving the Dual Problem
Getting the Primal Solution
Linear and Quadratic Programs
Exercises
Notes and References
Algorithms and Their Convergence
The Concept of an Algorithm.
Algorithms and Algorithmic Maps
Closed Maps and Convergence
Composition of Mappings
Comparison Among Algorithms
Exercises
Notes and References
Unconstrained Optimization.
Line Search Without Using Derivatives
Line Search Using Derivatives
Some Practical Line Search Methods
Closedness of the Line Search Algorithmic Map
Multidimensional Search Without Using Derivatives
Multidimensional Search Using Derivatives
Modification of Newton's Method: Levenberg-Marquardt and Trust Region Methods
Methods Using Conjugate Directions: Quasi-Newton and Conjugate Gradient Methods
Subgradient Optimization Methods
Exercises
Notes and References
Penalty and Barrier Functions.
Concept of Penalty Functions
Exterior Penalty Function Methods
Exact Absolute Value and Augmented Lagrangian Penalty Methods
Barrier Function Methods
Polynomial-Time Interior Point Algorithms for Linear Programming Based on a Barrier Function
Exercises
Notes and References
Methods of Feasible Directions.
Method of Zoutendijk
Convergence Analysis of the Method of Zoutendijk
Successive Linear Programming Approach
Successive Quadratic Programming or Projected Lagrangian Approach
Gradient Projection Method of Rosen
Reduced Gradient Method of Wolfe and Generalized Reduced Gradient Method
Convex-Simplex Method of Zangwill
Effective First- and Second-Order Variants of the Reduced Gradient Method
Exercises
Notes and References
Linear Complementary Problem, and Quadratic, Separable, Fractional, and Geometric Programming.
Linear Complementary Problem
Convex and Nonconvex Quadratic Programming: Global Optimization Approaches
Separable Programming
Linear Fractional Programming
Geometric Programming
Exercises
Notes and References
Mathematical Review.
Summary of Convexity, Optimality Conditions, and Duality.
Bibliography.
Index