Objectives of studying Optimization without constraints (Unconstrained optimization)

Objectives of studying Optimization without constraints (Unconstrained optimization):

Studying unconstrained optimization is crucial for understanding how to find the optimal values of a function without any restrictions on the decision variables. It helps develop essential mathematical tools and techniques, such as gradient-based methods, which are fundamental in many fields like machine learning, engineering, and economics. This area of study also lays the groundwork for tackling more complex constrained optimization problems and enables the development of efficient algorithms for solving real-world optimization tasks, from minimizing costs to maximizing performance in various applications.