Non-linear programming : a basic introduction /
Nita H. Shah and Poonam Prakash Mishra.
- First edition.
- 1 online resource (xi, 69 pages)
- Mathematical Engineering, Manufacturing, and Management Sciences Ser. .
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
"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"--