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E-raamat: Non-Linear Programming: A Basic Introduction [Taylor & Francis e-raamat]

, (Gujarat University, India)
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Non-Linear Programming: A Basic IntroductionSuurem pilt
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003105213
"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"--

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.

Preface vii
Acknowledgement ix
Author/Editor Biographies xi
Chapter 1 One-Dimensional Optimization Problem
1(14)
1.1 Introduction
1(1)
1.2 Analytical Approach
1(1)
1.3 Search Techniques
2(10)
1.3.1 Unrestricted Search Technique
3(1)
1.3.2 Exhaustive Search Technique
4(1)
1.3.3 Dichotomous Search Technique
4(2)
1.3.4 Fibonacci Search Method
6(2)
1.3.5 Golden Section Search Method
8(1)
1.3.6 Interpolation Method (Without Using Derivative)
9(1)
1.3.6.1 Quadratic Interpolation
9(3)
1.3.6.2 Cubic Interpolation
12(1)
1.4 Gradient-Based Approach
12(3)
1.4.1 Newton Method
12(1)
1.4.2 Secant Method
13(1)
Try Yourself
13(2)
Chapter 2 Unconstrained Multivariable Optimization
15(16)
2.1 Introduction
15(1)
2.2 Direct Search Methods
15(9)
2.2.1 Random Search Method
16(1)
2.2.2 Grid Search Method
16(1)
2.2.3 Univariate Search Method
17(1)
2.2.4 Pattern Search Algorithm
18(1)
2.2.4.1 Hooke--Jeeves Method
19(1)
2.2.4.2 Powell's Method
20(2)
2.2.5 Simplex Algorithm
22(2)
2.3 Gradient-Based Methods
24(7)
2.3.1 Using Hessian Matrix
24(1)
2.3.2 Steepest Descent Method
25(1)
2.3.3 Newton's Method
26(1)
2.3.4 Quasi Method
27(1)
Try Yourself
28(3)
Chapter 3 Constrained Multivariable Optimization
31(20)
3.1 Introduction
31(1)
3.2 Conventional Methods for Constrained Multivariate Optimization
31(10)
3.2.1 Problems with Equality Constraints
31(1)
3.2.1.1 Direct Substitution Method
32(1)
3.2.1.2 Lagrange Multipliers Method
33(5)
3.2.2 Problems with Inequality Constraints
38(1)
3.2.2.1 Kuhn--Tucker Necessary Conditions
38(1)
3.2.2.2 Kuhn--Tucker Sufficient Conditions
39(2)
3.3 Stochastic Search Techniques
41(10)
3.3.1 Genetic Algorithm
41(1)
3.3.1.1 Crossover
42(2)
3.3.2 Particle Swarm Optimization
44(1)
3.3.3 Hill Climbing Algorithm
45(1)
3.3.4 Simulated Annealing
45(2)
3.3.5 Ant Colony Optimization Algorithm
47(1)
3.3.6 Tabu Search Algorithm
48(2)
Try Yourself
50(1)
Chapter 4 Applications of Non-Linear Programming
51(18)
4.1 Basics of formulation
51(1)
4.2 Examples of NLP formulation
51(10)
4.3 Solving NLP through MATLAB Inbuilt Functions
61(6)
4.4 Choice of Method
67(2)
Try Yourself
67(2)
Index 69
Prof. Nita received her PhD in Statistics from Gujarat University in 1994. From February 1990 till now she is HOD of Department of Mathematics in Gujarat University, India. She is post-doctoral visiting research fellow of University of New Brunswick, Canada. Prof. Nita's research interests include inventory modeling in supply chain, robotic modeling, mathematical modeling of infectious diseases, image processing, dynamical systems and its applications etc. Prof. Nita has published 13 monograph, 5 textbooks, and 475+ peer-reviewed research papers. Four edited books were prepared for IGI-Global and Springer with a coeditor. Her papers are published in high impact Elsevier, Inderscience and Taylor and Francis journals. She is the author of 14 books.

Dr. Poonam Prakash Mishra has received her Ph. D degree in year 2010 in Mathematics and since then she is associated Pandit Deendayal Petroleum University. She also holds a masters degree in business administration (MBA) - operations management. Her core research area includes formulation, analysis and optimization of the problems using different Optimization Techniques. She has more than 30 publications with 8 chapters in edited books and made 10 papers presentation at national and international forum.
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