What is the sense of math and what is optimization

It is too later to write this note to think more about math and the important issue --optimization-- used in my research. 

In the research, we try to solve some problem comes from real world. For example, we need to design a new network to provide bandwidth to residential. What topology we should deploy constrained with cost of network elements. After implementation, how to adjust the network if the bandwidth is not enough? Most of problem in this world can be solved by optimization methods. 

 

We use mathematical concepts and constructions not simply to add rigor to the proceedings but because they are the language in terms of which calculation procedures are best developed, defined, and understood.

First of all, we need to establish the model of problem. In this model, we should correlate all the independent variables and define the performance criterion which we can evaluate according our expectation. We need to consider the boundaries of this model because it is a real scenario from reality. 

If all have been done, we choose some ways to solve this model, and find the best answer of this problem. There are many ways to solve optimization of engineering according different kind of model.

We can solve this model by describing in computing language, such as cplex. We can solve it without computer also.