Optimization
Optimization deals with finding the minimum value of a function. In the case of real-valued function optimization, the function maps vectors of real values to real values. The argument of the function usually represents a solution to a real-life problem. The result of the function is usually the evaluation of that solution, that is, a numerical estimate of how well the solution in question solves the problem. The global minimum
is defined as the function argument (a vector) that gives the lowest (or highest) function value. That is, there has to be no other argument vector that would result in a function value that is lower or higher.
Most often, optimization methods do not guarantee finding the global minimum, and you have to settle for a local minimum. A local minimum is the solution that minimizes the function within some local area of the function surface (although don't quote that definition anywhere). You can look up more information about optimization in literature...