An Interval Method for Global Unconstrained Optimization
Christian Jansson · 1992
A method for calculating the global minimum points of an unconstrained minimization problem min{f(x) | x ∈ X{ is presented. f: X → ℝ and $$ K = \frac{{k\varrho g}}{\eta } $$ is an interval vector, i.e. a compact parallelepiped with sides parallel to the coordinate axes. This method is based on the tools of interval arithmetic and uses a special branch-and-bound technique in connection with a descent method. Besides the calculation of approximations of the global minimum value f* and the set of all global minimum points X* the algorithm provides a guaranteed lower and upper bound of f*, i.e. the bounds calculated on a computer are always correct despite the presence of rounding errors and the nonlinearity of f. Derivatives of the function are not required.