Non-Linear Programming: A Basic Introduction

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