This study presents an effective global optimization technique designed for multivariate functions that are Hölder continuous. Unlike traditional methods that construct lower bounding proxy functions, this algorithm employs a predetermined query creation rule that makes it computationally superior. The algorithm's performance is assessed using the average or cumulative regret, which also implies a bound for the simple regret and reflects the overall effectiveness of the approach. The results show that with appropriate parameters the algorithm attains an average regret bound of $O(T^{-\fracα{n}})$ for optimizing a Hölder continuous target function with Hölder exponent $α$ in an $n$-dimensional space within a given time horizon $T$. We demonstrate that this bound is minimax optimal.