  PDE-constrained optimization problems have been barely solved by radial basis
functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can
attain an exponential rate of convergence when $C^{\infty}$ kernels are used,
also, these techniques, which are truly scattered, are known to be flexible to
discretize complex boundaries in several dimensions. On the other hand,
exponential convergence implies an exponential growth of the condition number
of the Gram matrix associated with these meshfree methods and global
collocation techniques are known to be computationally expensive. In this
paper, and in the context of optimal constrained optimization problems, we aim
to explore a possible answer to both problems. Specifically, we introduce two
local RBF methods: LAM-DQ based in the combination of an asymmetric local
method (LAM), inspired in local Hermite interpolation (LHI), with the
differential quadrature method (DQ), and LAM-LAM which use two times the local
asymmetric method. The efficiency of these local methods against global
collocation by solving several synthetic convection-diffusion control problems
is analyzed. In this article, we also propose a preconditioning technique and
treat the ill-conditioning problem by using extended arithmetic precision. We
think that these local methods, which are highly parallelizable, shows a
possible way to solve massive optimization control problems in an efficient
way.
