General issues for optimization problems

There are several issues in optimization. The most important one is how to choose an appropriate objective function. For some cases, the objective function is obvious. Unfortunately, for other cases, it is not that crystal clear. Since choosing a good objective depends on the specific situation, we will discuss it further, but remember that an appropriate objective function might make our task much easier.

In many cases, an inappropriate objective function might cause the following problems:

• It is difficult to find a feasible solution
• We might end up with a local solution
• We might have a corner solution
• It takes a long time to converge (that is, too much computation time to find a good solution)

Let's look at a convex function; the code and corresponding graph are given here:

x<-seq(-10,10,0.1) 
a<-4 
b<- -2 
c<-10 
y...