Abstract: | Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in
p
,
n
, respectively, Z is a closed convex set in p+n, while G is the complement of an open convex set in
n
. The function c:
p+n
is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in
n
. Computational experiments show that the resulting algorithms work well for problems with smalln. |