ISBN 9788126540440,Engineering Optimization: Theory and Practice

Engineering Optimization: Theory and Practice



Wiley India Pvt Ltd

Publication Year 2013

ISBN 9788126540440

ISBN-10 8126540443

Paper Back

Edition 4th
Number of Pages 836 Pages
Language (English)

Basic Engineering

Table of Contents
Introduction to Optimization.

• Historical Development.
• Engineering Applications of Optimization.
• Statement of an Optimization Problem.
• Classification of Optimization Problems.
• Optimization Techniques.
• Engineering Optimization Literature.
• Solution of Optimization Problems Using MATLAB.

Classical Optimization Techniques.

• Single-Variable Optimization.
• Multivariable Optimization with No Constraints.
• Multivariable Optimization with Equality Constraints.
• Multivariable Optimization with Inequality Constraints.
• Convex Programming Problem.

Linear Programming I: Simplex Method.

• Applications of Linear Programming.
• Standard Form of a Linear Programming Problem.
• Geometry of Linear Programming Problems.
• Definitions and Theorems.
• Solution of a System of Linear Simultaneous Equations.
• Pivotal Reduction of a General System of Equations.
• Motivation of the Simplex Method.
• Simplex Algorithm.
• Two Phases of the Simplex Method.
• MATLAB Solution of LP Problems.

Linear Programming II: Additional Topics and Extensions.

• Revised Simplex Method.
• Duality in Linear Programming.
• Decomposition Principle.
• Sensitivity or Postoptimality Analysis.
• Transportation Problem.
• Karmarkar's Interior Method.
• Quadratic Programming.
• MATLAB Solutions.

Nonlinear Programming I: One-Dimensional Minimization Methods.

• Unimodal Function.
• Elimination Methods.
• Unrestricted Search.
• Exhaustive Search.
• Dichotomous Search.
• Interval Halving Method.
• Fibonacci Method.
• Golden Section Method.
• Comparison of Elimination Methods.

Interpolation Methods.

• Quadratic Interpolation Method.
• Cubic Interpolation Method.
• Direct Root Methods.
• Practical Considerations.
• MATLAB Solution of One-Dimensional Minimization Problems.

Nonlinear Programming II: Unconstrained Optimization Techniques.

• Direct Search Methods.
• Random Search Methods.
• Grid Search Method.
• Univariate Method.
• Pattern Directions.
• Powell's Method.
• Simplex Method.

Indirect Search (Descent) Methods.

• Gradient of a Function.
• Steepest Descent (Cauchy) Method.
• Conjugate Gradient (Fletcher--Reeves) Method.
• Newton's Method.
• Marquardt Method.
• Quasi-Newton Methods.
• Davidon--Fletcher--Powell Method.
• Broyden--Fletcher--Goldfarb--Shanno Method.
• Test Functions.
• MATLAB Solution of Unconstrained Optimization Problems.

Nonlinear Programming III: Constrained Optimization Techniques.

• Characteristics of a Constrained Problem.

Direct Methods.

• Random Search Methods.
• Complex Method.
• Sequential Linear Programming.
• Basic Approach in the Methods of Feasible Directions.
• Zoutendijk's Method of Feasible Directions.
• Rosen's Gradient Projection Method.
• Generalized Reduced Gradient Method.
• Sequential Quadratic Programming.

Indirect Methods.

• Transformation Techniques.
• Basic Approach of the Penalty Function Method.
• Interior Penalty Function Method.
• Convex Programming Problem.
• Exterior Penalty Function Method.
• Extrapolation Techniques in the Interior Penalty Function Method.
• Extended Interior Penalty Function Methods.
• Penalty Function Method for Problems with Mixed Equality and Inequality Constraints.
• Penalty Function Method for Parametric Constraints.
• Augmented Lagrange Multiplier Method.
• Checking the Convergence of Constrained Optimization Problems.
• Test Problems.
• MATLAB Solution of Constrained Optimization Problems