This book is for beginners who are struggling to understand and optimize non-linear problems. The content will help readers gain an understanding and learn how to formulate real-world problems and will also give insight to many researchers for their future prospects.
It proposes a mind map for conceptual understanding and includes sufficient solved examples for reader comprehension. The theory is explained in a lucid way. The variety of examples are framed to raise the thinking level of the reader and the formulation of real-world problems are included in the last chapter along with applications.
The book is self-explanatory, well synchronized and written for undergraduate, post graduate and research scholars.
Author(s): Nita H. Shah, Poonam Prakash Mishra
Series: Mathematical Engineering, Manufacturing, and Management Sciences
Publisher: CRC Press
Year: 2020
Language: English
Pages: 82
City: Boca Raton
Cover
Half Title
Series Information
Title Page
Copyright Page
Table of contents
Preface
Acknowledgement
Author/Editor Biographies
1 One-Dimensional Optimization Problem
1.1 Introduction
1.2 Analytical Approach
1.3 Search Techniques
1.3.1 Unrestricted Search Technique
1.3.2 Exhaustive Search Technique
1.3.3 Dichotomous Search Technique
1.3.4 Fibonacci Search Method
1.3.5 Golden Section Search Method
1.3.6 Interpolation Method (Without Using Derivative)
1.3.6.1 Quadratic Interpolation
1.3.6.2 Cubic Interpolation
1.4 Gradient-Based Approach
1.4.1 Newton Method
1.4.2 Secant Method
Try Yourself
2 Unconstrained Multivariable Optimization
2.1 Introduction
2.2 Direct Search Methods
2.2.1 Random Search Method
2.2.2 Grid Search Method
2.2.3 Univariate Search Method
2.2.4 Pattern Search Algorithm
2.2.4.1 Hooke–Jeeves Method
2.2.4.2 Powell’s Method
2.2.5 Simplex Algorithm
2.3 Gradient-Based Methods
2.3.1 Using Hessian Matrix
2.3.2 Steepest Descent Method
2.3.3 Newton’s Method
2.3.4 Quasi Method
Try Yourself
3 Constrained Multivariable Optimization
3.1 Introduction
3.2 Conventional Methods for Constrained Multivariate Optimization
3.2.1 Problems with Equality Constraints
3.2.1.1 Direct Substitution Method
3.2.1.2 Lagrange Multipliers Method
3.2.2 Problems with Inequality Constraints
3.2.2.1 Kuhn–Tucker Necessary Conditions
3.2.2.2 Kuhn–Tucker Sufficient Conditions
3.3 Stochastic Search Techniques
3.3.1 Genetic Algorithm
3.3.1.1 Crossover
3.3.2 Particle Swarm Optimization
3.3.3 Hill Climbing Algorithm
3.3.4 Simulated Annealing
3.3.5 Ant Colony Optimization Algorithm
3.3.6 Tabu Search Algorithm
Try Yourself
4 Applications of Non-Linear Programming
4.1 Basics of Formulation
4.2 Examples of NLP Formulation
Example 1: Profit Maximization – Production Problem
Example 2: Cost Minimization – Optimum Designing Problem
Example 3: Cost Minimization – Electrical Engineering
Example 4: Design of a Small Heat Exchanger Network – Chemical Engineering
Example 5: Real-Time Optimization of a Distillation Column – Petroleum Engineering
4.3 Solving NLP through MATLAB Inbuilt Functions
4.4 Choice of Method
Try Yourself
Bibliography
Index
