Description: Non-linear optimization algorithms are mathematical and computational tools designed to solve problems where the objective function or constraints are non-linear. Unlike linear optimization, which relies on linear relationships between variables, non-linear optimization addresses more complex situations where interactions between variables can be quadratic, cubic, or of higher order. These algorithms are essential in various disciplines as they allow for finding optimal solutions in scenarios where relationships are not straightforward. The main characteristics of these algorithms include the ability to handle multiple variables, flexibility to adapt to different types of functions, and the capability to explore non-convex solution spaces. The relevance of non-linear optimization algorithms lies in their application to real-world problems, such as engineering, economics, and operations research, where decisions must be made under conditions of uncertainty and complexity. Their development has been driven by the need to solve problems that cannot be adequately addressed by linear methods, making them a fundamental tool in the optimization of complex systems.
