About Us

Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc

More about us

Keep Connect with Us

  • =

Login to Your Account

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
    3.4 Quadratic Forms
    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
    5.5 Level Sets and Gradients
    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. Gradient Methods
    8.1 Introduction
    8.2 The Method of Steepest Descent
    8.3 Analysis of Gradient Methods
    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
    10.3 The Conjugate Gradient Algorithm
    10.4 The Conjugate Gradient Algorithm for Nonquadratic
    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
    14.2 The Nelder-Mead Simplex Algorithm
    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

  • Download Free PDF
    Download Similar Books

    other Math Books of NUMERICAL ANALYSIS

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