  DIviding RECTangles (DIRECT) is an efficient and popular method in dealing
with bound constrained optimization problems. However, DIRECT suffers from
dimension curse, since its computational complexity soars when dimension
increases. Besides, DIRECT also converges slowly when the objective function is
flat. In this paper, we propose a coordinate DIRECT algorithm, which coincides
with the spirits of other coordinate update algorithms. We transform the
original problem into a series of sub-problems, where only one or several
coordinates are selected to optimize and the rest keeps fixed. For each
sub-problem, coordinately dividing the feasible domain enjoys low computational
burden. Besides, we develop adaptive schemes to keep the efficiency and
flexibility to tackle different functions. Specifically, we use block
coordinate update, of which the size could be adaptively selected, and we also
employ sequential quadratic programming (SQP) to conduct the local search to
efficiently accelerate the convergence even when the objective function is
flat. With these techniques, the proposed algorithm achieves promising
performance on both efficiency and accuracy in numerical experiments.
