Principles of Optimization

Author: Zhiming Ou

Publisher:    3265 Public Way

ISBN: 978-1-0677470-0-8

Summary

By examining all the means for finding the optimal values of a quantity, starting from the fundamental inequalities, the geometric intuition, linear programs, to Lagrange multiplier, and the method of variation, I revised Newton’s Laws of, and revealed the distribution of energy in space, and understand that, in the microworld, the nature only leaves us with probability distribution.

Through reading this book, one can understand the nature of the world: thrifty or greedy? That’s the major problem. Every entity in the universe has a kind of wisdom: it knows when and how to make a change. We need to use math to describe things quantitatively, only in this way, we could know how does the universe run.

 

Content

Chapter 1 Inequality         3

• 1 Axioms

     Proving inequalities        4

• 2 Named Inequalities 6
• 3 Ranges of Functions 13

 

Chapter 2 Geometric Optimal Values       17

• 1 Shortest route 18

      The triangle Inequality

• 2 Some Economical shapes 22
• 3 Orthogonal vectors 24

 

Chapter 3 Linear Programming       26

• 1 Linear Programming for Two Variables 27
• 2 Three or more variables 32

 

Chapter 4 Optimizing Single Variable      35

• 1 Fermat’s Theorem 35
• 2 Proving Inequalities 39

 

Chapter 5 Optimizing Multiple Variables

• 1 Local and Global Extreme Values 42
• 2 Conditionally Optimal Values 50

 

Chapter 6 Extreme Values of Integrals        54

• 1 The method of Variation 54
• 2 Geodesic 59
• 3 Minimal and Maximal Surface 62

 

Chapter 7 Thrifty or Greedy        63

• 1 Energy distribution in a region 63
• 2 Principle of Uncertainty 70