Eva Eggeling and Dieter W. Fellner and Torsten Ullrich
Probability of Globality
36 - 40
2013
7
1
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/6040
https://publications.waset.org/vol/73
World Academy of Science, Engineering and Technology
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 soughtafter, 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.
Open Science Index 73, 2013