  A gradient-free deterministic method is developed to solve global
optimization problems for Lipschitz continuous functions defined in arbitrary
path-wise connected compact sets in Euclidean spaces. The method can be
regarded as granular sieving with synchronous analysis in both the domain and
range of the objective function. With straightforward mathematical formulation
applicable to both univariate and multivariate objective functions, the global
minimum value and all the global minimizers are located through two decreasing
sequences of compact sets in, respectively, the domain and range spaces. The
algorithm is easy to implement with moderate computational cost. The method is
tested against extensive benchmark functions in the literature. The
experimental results show remarkable effectiveness and applicability of the
algorithm.
