Description: Unconstrained optimization refers to a type of optimization problem where the goal is to maximize or minimize an objective function without any constraints imposed on the decision variables. In this context, the variables can take any value within their domain, allowing for greater flexibility in the search for optimal solutions. This approach is fundamental in various areas of mathematics and engineering, as it enables a broader exploration of the solution space. The main characteristics of unconstrained optimization include the absence of conditions that limit the range of the variables, which facilitates the application of optimization algorithms such as gradient descent, Newton’s method, and evolutionary algorithms. The relevance of this type of optimization lies in its ability to tackle complex problems where constraints may be difficult to define or where a solution is sought in a high-dimensional space. In practice, unconstrained optimization is used in the adjustment of mathematical models, the calibration of systems, and in the optimization of processes, where the best possible configuration needs to be found without being limited by external constraints.
