Branch and bound methods in Global Optimization guarantee to find the set of global minimum points up to a certain accuracy. Partition sets typically take the shape of boxes, cones and simplices. In the tradition of interval arithmetic for generating bounds on box shaped partition sets, the concept of monotonicity test is used in order to reduce dimension. This paper shows how such a concept can be extended to simplicial partition sets and how to elaborate it for the Standard Quadratic Program.

1.
R.
Horst
and
H.
Tuy
,
Global Optimization (Deterministic Approaches)
(
Springer
,
Berlin
,
1990
).
2.
E. M. T.
Hendrix
and
B. G.-.
Tóth
,
Introduction to Nonlinear and Global Optimization
(
Springer
,
New York
,
2010
).
3.
R.
Paulavičius
and
J.
Žilinskas
,
Simplicial Global Optimization
(
Springer
,
New York
,
2014
).
4.
R. E.
Moore
,
Interval analysis
(
Prentice-Hall
,
New Jersey
,
1966
).
5.
E.
Hansen
, Global Optimization Using Interval Analysis,
Pure and Applied Mathematics
, Vol.
165
(
Marcel Dekker
,
Inc, New York
,
1992
).
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