Non-Linear Programming

A Basic Introduction

Nita H. Shah, Poonam Prakash Mishra

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9780367613280
• eBook ISBN: 9781000339956
• Topic: Business
• Subtopic: Operations
• Index: Business

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.

1

One-Dimensional Optimization Problem

1.1Introduction

In this section, we discuss the different methods available to optimize (minimize/maximize) the given function with only one variable. Methods used for one-dimensional optimization are highly useful for multivariable optimization. Firstly, we see the methods that can be used for unimodal functions. Unimodal functions are those functions that has only one peak or valley (in the given domain). Mathematically, function f(x) is unimodal if (i)x1<x2<x* implies that f(x2)<f(x1) and (ii)x2>x1>x* implies that f(x1)<f(x2), where x* is the minimum point. Figure 1.1 is a mind map that can help to explore available methods for these set of problems.

Figure 1.1Tree diagram of available methods for one-variable optimization.

1.2Analytical Approach

Analytic or conventional approach for extreme values can be achieved by following necessary and sufficient conditions, but t...

Table of contents

• Cover
• Half Title
• Series Information
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgement
• Author/Editor Biographies
• 1 One-Dimensional Optimization Problem
• 2 Unconstrained Multivariable Optimization
• 3 Constrained Multivariable Optimization
• 4 Applications of Non-Linear Programming
• Index