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### Introduction to Optimization Fourth Edition by Edwin K. P. Chong and Stanislaw H. Zak

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Numerical Analysis eBooks . We hope mathematician or person who’s interested in mathematics like these books. Introduction to Optimization (Fourth Edition) written by Edwin K. P. Chong , Colorado State University Stanislaw H. Zak, Purdue University . This is an other book of mathematics cover the following topics.

• PART I MATHEMATICAL REVIEW

• 1. Methods of Proof and Some Notation
1.1 Methods of Proof
1.2 Notation
Exercises

• 2. Vector Spaces and Matrices
2.1 Vector and Matrix
2.2 Rank of a Matrix
2.3 Linear Equations
2.4 Inner Products and Norms
Exercises

• 3. Transformations
3.1 Linear Transformations
3.2 Eigenvalues and Eigenvectors
3.3 Orthogonal Projections
3.5 Matrix Norms
Exercises

• 4. Concepts from Geometry
4.1 Line Segments
4.2 Hyperplanes and Linear Varieties
4.3 Convex Sets
4.4 Neighborhoods
4.5 Poly topes and Polyhedra
Exercises

• 5. Elements of Calculus
5.1 Sequences and Limits
5.2 Differentiability
5.3 The Derivative Matrix
5.4 Differentiation Rules
5.6 Taylor Series
Exercises

• PART II UNCONSTRAINED OPTIMIZATION

• 6. Basics of Set-Constrained and Unconstrained Optimization
6.1 Introduction
6.2 Conditions for Local Minimizers
Exercises

• 7. One-Dimensional Search Methods
7.1 Introduction
7.2 Golden Section Search
7.3 Fibonacci Method
7.4 Bisection Method
7.5 Newtons Method
7.6 Secant Method
7.7 Bracketing
7.8 Line Search in Multidimensional Optimization
Exercises

8.1 Introduction
8.2 The Method of Steepest Descent
Exercises

• 9. Newton's Method
9.1 Introduction
9.2 Analysis of Newton's Method
9.3 Levenberg-Marquardt Modification
9.4 Newton's Method for Nonlinear Least Squares
Exercises

• 10. Conjugate Direction Methods
10.1 Introduction
10.2 The Conjugate Direction Algorithm
Problems
Exercises

• 11. Quasi-Newton Methods
11.1 Introduction
11.2 Approximating the Inverse Hessian
11.3 The Rank One Correction Formula
11.4 The DFP Algorithm
11.5 The BFGS Algorithm
Exercises

• 12. Solving Linear Equations
12.1 Least-Squares Analysis
12.2 The Recursive Least-Squares Algorithm
12.3 Solution to a Linear Equation with Minimum Norm
12.4 Kaczmarzs Algorithm
12.5 Solving Linear Equations in General
Exercises

• 13. Unconstrained Optimization and Neural Networks
13.1 Introduction
13.2 Single-Neuron Training
13.3 The Backpropagation Algorithm
Exercises

• 14. Global Search Algorithms
14.1 Introduction
14.3 Simulated Annealing
14.4 Particle Swarm Optimization
14.5 Genetic Algorithms
Exercises

• PART III LINEAR PROGRAMMING

• 15. Introduction to Linear Programming
15.1 Brief History of Linear Programming
15.2 Simple Examples of Linear Programs
15.3 Two-Dimensional Linear Programs
15.4 Convex Polyhedra and Linear Programming
15.5 Standard Form Linear Programs
15.6 Basic Solutions
15.7 Properties of Basic Solutions
15.8 Geometric View of Linear Programs
Exercises

• 16. Simplex Method
16.1 Solving Linear Equations Using Row Operations
16.2 The Canonical Augmented Matrix
16.3 Updating the Augmented Matrix
16.4 The Simplex Algorithm
16.5 Matrix Form of the Simplex Method
16.6 Two-Phase Simplex Method
16.7 Revised Simplex Method
Exercises

• 17. Duality
17.1 Dual Linear Programs
17.2 Properties of Dual Problems
Exercises

• 18. Nonsimplex Methods
18.1 Introduction
18.2 Khachiyan's Method
18.3 Affine Scaling Method
18.4 Karmarkar's Method Exercises

• 19. Integer Linear Programming
19.1 Introduction
19.2 Unimodular Matrices
19.3 The Gomory Cutting-Plane Method
Exercises

• PART IV NONLINEAR CONSTRAINED OPTIMIZATION

• 20. Problems with Equality Constraints
20.1 Introduction
20.2 Problem Formulation
20.3 Tangent and Normal Spaces
20.4 Lagrange Condition
20.5 Second-Order Conditions
20.6 Minimizing Quadratics Subject to Linear Constraints
Exercises

• 21. Problems with Inequality Constraints
21.1 Karush-Kuhn-Tucker Condition
21.2 Second-Order Conditions
Exercises

• 22. Convex Optimization Problems
22.1 Introduction
22.2 Convex Functions
22.3 Convex Optimization Problems
22.4 Semidefinite Programming
Exercises

• 23. Algorithms for Constrained Optimization
23.1 Introduction
23.2 Projections
23.3 Projected Gradient Methods with Linear Constraints
23.4 Lagrangian Algorithms
23.5 Penalty Methods
Exercises

• 24. Multiobjective Optimization
24.1 Introduction
24.2 Pareto Solutions
24.3 Computing the Pareto Front
24.4 From Multiobjective to Single-Objective Optimization
24.5 Uncertain Linear Programming Problems
Exercises

• References

• Index

• ##### other Math Books of NUMERICAL ANALYSIS

Numerical Analysis by L. Ridgway Scott
• Free
• English
• PDF 55
• Page 341
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