Introduction to Optimization

The optimization process either minimizes or maximizes the objective function f(x) until reaching the optimal value for f(x). When minimizing f(x), the optimal solution x* ∈ X satisfies the following condition.

The optimization process searches for the value of x* that minimizes f(x), subject to the constraint x* ∈ X, where X is the constraint set. A value that satisfies the conditions defined in the previous equation is a global minimum.

In the case of maximization, x* satisfies the following condition.

A value satisfying the preceding condition is a global maximum.