What is numerical optimization?

Numerical optimization is a branch of mathematics and computer science that seeks to find the best solution to a problem, where "best" is defined by an objective function. This function depends on one or more variables which may be subject to constraints. Numerical optimization algorithms iteratively refine a candidate solution until a satisfactory solution is found, often by finding a minimum or maximum value of the objective function. Common applications include machine learning (training models), engineering design (optimizing performance), finance (portfolio optimization), and operations research (scheduling and logistics).