In the field of global optimization, many existing algorithms face challenges
posed by non-convex target functions and high computational complexity or
unavailability of gradient information. These limitations, exacerbated by
sensitivity to initial conditions, often lead to suboptimal solutions or failed
convergence. This is true even for Metaheuristic algorithms designed to
amalgamate different optimization techniques to improve their efficiency and
robustness. To address these challenges, we develop a sequence of
multidimensional integration-based methods that we show to converge to the
global optima under some mild regularity conditions. Our probabilistic approach
does not require the use of gradients and is underpinned by a mathematically
rigorous convergence framework anchored in the nuanced properties of nascent
optima distribution. In order to alleviate the problem of multidimensional
integration, we develop a latent slice sampler that enjoys a geometric rate of
convergence in generating samples from the nascent optima distribution, which
is used to approximate the global optima. The proposed Probabilistic Global
Optimizer (ProGO) provides a scalable unified framework to approximate the
global optima of any continuous function defined on a domain of arbitrary
dimension. Empirical illustrations of ProGO across a variety of popular
non-convex test functions (having finite global optima) reveal that the
proposed algorithm outperforms, by order of magnitude, many existing
state-of-the-art methods, including gradient-based, zeroth-order gradient-free,
and some Bayesian Optimization methods, in term regret value and speed of
convergence. It is, however, to be noted that our approach may not be suitable
for functions that are expensive to compute