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.

翻译：开发了一种无梯度的确定方法,以解决Lipschitz连续功能的全球优化问题,这些功能的定义是在欧几里德空间任意的路径连接的紧凑装置中任意界定的。该方法可被视为与目标功能领域和范围的同步分析同步的粒子筛选。如果直接的数学公式既适用于单向和多变量目标功能,则全球最低值和所有全球最小化器分别通过在域和范围空间的两个递减的紧凑装置序列定位。该算法很容易以适度的计算成本执行。该方法根据文献中的广泛基准函数进行测试。实验结果显示了算法的显著有效性和适用性。