Open Science Research Excellence
%0 Journal Article
%A Eva Eggeling and  Dieter W. Fellner and  Torsten Ullrich
%D 2013 
%J  International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
%B World Academy of Science, Engineering and Technology
%I International Science Index 73, 2013
%T Probability of Globality
%V 73
%X The objective of global optimization is to find the
globally best solution of a model. Nonlinear models are ubiquitous
in many applications and their solution often requires a global
search approach; i.e. for a function f from a set A ⊂ Rn to
the real numbers, an element x0 ∈ A is sought-after, such that
∀ x ∈ A : f(x0) ≤ f(x). Depending on the field of application,
the question whether a found solution x0 is not only a local minimum
but a global one is very important.
This article presents a probabilistic approach to determine the
probability of a solution being a global minimum. The approach is
independent of the used global search method and only requires a
limited, convex parameter domain A as well as a Lipschitz continuous
function f whose Lipschitz constant is not needed to be known.
%P 36 - 40