Is there any gradient descent based technique for searching absolute minimum (maximum) of a function in multidimensional space?
I presume you are talking about unconstrained minimization. Your question should specify if you are considering a specific problem structure. Otherwise, the answer is no.

First I should dispel a myth. The classical gradient descent method (also called steepest descent method) is not even guaranteed to find a local minimizer. It stops when it has found a first-order critical point, i.e., one where the gradient vanishes. Depending on the particular function being minimized and the starting point, you may very well end up at a saddle point or even at a global maximizer!

Consider for instance $f(x,y) = x^2 - y^2$ and the initial point $(x_0,y_0) := (1,0)$. The steepest descent direction is $-\nabla f(1,0) = (-2,0)$. One step of the method with exact line search leaves you at $(0,0)$ where the gradient vanishes. Alas, it's a saddle point. You would realize by examining the second-order optimality conditions. But now imagine the function is $f(x,y) = x^2 - 10^{-16} y^2$. Here, $(0,0)$ is still a saddle point, but numerically, the second-order conditions may not tell you. In general, say you determine that the Hessian $\nabla^2 f(x^*,y^*)$ has an eigenvalue equal to $-10^{-16}$. How do you read it? Is it negative curvature or numerical error? How about $+10^{-16}$?

Consider now a function such as
$$
f(x) =
\begin{cases}
 1 &amp; \text{if } x \leq 0 \\
\cos(x) &amp; \text{if } 0 &lt; x &lt; \pi \\
-1 &amp; \text{if } x \geq \pi.
\end{cases}
$$

This function is perfectly smooth, but if your initial point is $x_0 = -2$, the algorithm stops at a global maximizer. And by checking the second-order optimality conditions, you wouldn't know! The problem here is that some local minimizers are global maximizers!

Now virtually all gradient-based optimization methods suffer from this by design. Your question is really about global optimization. Again, the answer is no, there are no general recipes to modify a method so as to guarantee that a global minimizer is identified. Just ask yourself: if the algorithm returns a value and says it is a global minimizer, how would you check that it's true?

There are classes of methods in global optimization. Some introduce randomization. Some use multi-start strategies. Some exploit the structure of the problem, but those are for special cases. Pick up a book on global optimization. You will enjoy it.