What is optimization? Roughly speaking, optimization is to minimize or maximize a function (which is called the objective function) under some constraints.
For example, we some several ways to return the campus from Hongqiao Station: by taxi (Didi / Gaode), by metro or by bus (Hongqiao 4 Line / Min-Hong 2 Line), etc. We would like to minimize the time, but our money is limited. This is an optimization problem.
Formally, an optimization problem can be defined by
Suppose there are
For each
Consider the free falling motion. The height and the time of a free fall follow the law
Suppose we have the following data and we would like to use
10 | 20 | 30 | 40 | |
---|---|---|---|---|
1.011 | 2.019 | 3.032 | 4.041 |
However, before solving this problem, we should first ask the following question: if we choose a certain value of
Generally, we have the following question. Let
If we only have two numbers
We need to extend the concept of the absolute value to measure the distances between vectors in
Given a vector space
1. (Nonnegativity)
2. (Positive definiteness)
3. (Absolute homogeneity)
4. (Triangle inequality)