TY - JFULL
AU - Eva Eggeling and Dieter W. Fellner and Torsten Ullrich
PY - 2013/2/
TI - Probability of Globality
T2 - International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
SP - 35
EP - 40
EM - torsten.ullrich@fraunhofer.at
VL - 7
SN - 1307-6892
UR - http://waset.org/publications/6040
PU - World Academy of Science, Engineering and Technology
NX - International Science Index 73, 2013
N2 - 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.
ER -