Fundamentals of optimization techniques with algorithms /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Nayak, Sukanta (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: London, United Kingdom ; San Diego, CA, United States : Academic Press is an imprint of Elsevier, [2020]
Temas:
Mathematical optimization.
Computer algorithms.
Algorithms.
Algorithms
Algorithmes.
Optimisation math�ematique.
algorithms.
Computer algorithms
Mathematical optimization
e-books.
Livres num�eriques.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • Fundamentals of Optimization Techniques With Algorithms
  • Copyright Page
  • Dedication
  • Contents
  • Preface
  • Acknowledgments
  • 1. Introduction to optimization
  • 1.1 Optimal problem formulation
  • 1.1.1 Design variables
  • 1.1.2 Constraints
  • 1.1.3 Objective function
  • 1.1.4 Variable bounds
  • 1.2 Engineering applications of optimization
  • 1.3 Optimization techniques
  • Further reading
  • 2. Linear programming
  • 2.1 Formulation of the problem
  • Practice set 2.1
  • 2.2 Graphical method
  • 2.2.1 Working procedure
  • Practice set 2.2
  • 2.3 General LPP
  • 2.3.1 Canonical and standard forms of LPP
  • Practice set 2.3
  • 2.4 Simplex method
  • 2.4.1 Reduction of feasible solution to a basic feasible solution
  • 2.4.2 Working procedure of the simplex method
  • Practice set 2.4
  • 2.5 Artificial variable techniques
  • 2.5.1 Big M method
  • 2.5.2 Two-phase method
  • Practice set 2.5
  • 2.6 Duality Principle
  • 2.6.1 Formulation of a dual problem
  • 2.6.1.1 Formulation of a dual problem when the primal has equality constraints
  • 2.6.1.2 Duality principle
  • Practice set 2.6
  • 2.7 Dual simplex method
  • 2.7.1 Working procedure for a dual simplex method
  • Practice set 2.7
  • Further reading
  • 3. Single-variable nonlinear optimization
  • 3.1 Classical method for single-variable optimization
  • 3.2 Exhaustive search method
  • 3.3 Bounding phase method
  • 3.4 Interval halving method
  • 3.5 Fibonacci search method
  • 3.6 Golden section search method
  • 3.7 Bisection method
  • 3.8 Newton-Raphson method
  • 3.9 Secant method
  • 3.10 Successive quadratic point estimation method
  • Further reading
  • 4. Multivariable unconstrained nonlinear optimization
  • 4.1 Classical method for multivariable optimization
  • 4.1.1 Definition: rth differential of a function f(X)
  • 4.1.2 Necessary condition
  • 4.1.3 Sufficient condition
  • 4.2 Unidirectional search method
  • 4.3 Evolutionary search method
  • 4.3.1 Box's evolutionary optimization method
  • 4.4 Simplex search method
  • 4.5 Hooke-Jeeves pattern search method
  • 4.5.1 Exploratory move
  • 4.5.2 Pattern move
  • 4.6 Conjugate direction method
  • 4.6.1 Parallel subspace property
  • 4.6.2 Extended parallel subspace property
  • 4.7 Steepest descent method
  • 4.7.1 Cauchy's (steepest descent) method
  • 4.8 Newton's method
  • 4.9 Marquardt's method
  • Practice set
  • Further reading
  • 5. Multivariable constrained nonlinear optimization
  • 5.1 Classical methods for equality constrained optimization
  • 5.1.1 Solution by direct substitution
  • 5.1.2 Solution by the method of constrained variation
  • 5.1.3 Solution by the method of Lagrange multipliers
  • 5.1.3.1 Necessary conditions
  • 5.1.3.2 Sufficient condition
  • 5.2 Classical methods for inequality constrained optimization
  • 5.3 Random search method
  • 5.4 Complex method
  • 5.4.1 Iterative procedure
  • 5.5 Sequential linear programming
  • 5.6 Zoutendijk's method of feasible directions

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