Deterministic global optimization

Deterministic global optimization is a branch of numerical optimization which focuses on finding the global solutions of an optimization problem whilst providing theoretical guarantees that the reported solution is indeed the global one, within some predefined tolerance. The term 'deterministic global optimization' typically refers to complete or rigorous (see below) optimization methods. Rigorous methods converge to the global optimum in finite time. Deterministic global optimization methods are typically used when locating the global solution is a necessity (i.e. when the only naturally occurring state described by a mathematical model is the global minimum of an optimization problem), when it is extremely difficult to find a feasible solution, or simply when the user desires to locate the best possible solution to a problem. Deterministic global optimization is a branch of numerical optimization which focuses on finding the global solutions of an optimization problem whilst providing theoretical guarantees that the reported solution is indeed the global one, within some predefined tolerance. The term 'deterministic global optimization' typically refers to complete or rigorous (see below) optimization methods. Rigorous methods converge to the global optimum in finite time. Deterministic global optimization methods are typically used when locating the global solution is a necessity (i.e. when the only naturally occurring state described by a mathematical model is the global minimum of an optimization problem), when it is extremely difficult to find a feasible solution, or simply when the user desires to locate the best possible solution to a problem. Neumaier classified global optimization methods in four categories, depending on their degree of rigour with which they approach the optimum, as follows: