  For solving pseudo-convex global optimization problems, we present a novel
fully adaptive steepest descent method (or ASDM) without any hard-to-estimate
parameters. For the step-size regulation in an $\varepsilon$-normalized
direction, we use the deterministic rules, which were proposed in J. Optim.
Theory Appl. (2019,\, DOI: 10.1007/S10957-019-01585-W).
  We obtained the optimistic convergence estimates for the generated by ASDM
sequence of iteration points. Namely, the sequence of function values of
iterates has the advantage of the strict monotonic behaviour and globally
converges to the objective function optimum with the sublinear rate. This rate
of convergence is now known to be the best for the steepest descent method in
the non-convex objectives context. Preliminary computational tests confirm the
efficiency of the proposed method and low computational costs for its
realization.
