Multidimensional multiextremal optimization problems and numerical methods for solving them are studied. The objective function is supposed to satisfy the Lipschitz condition with an a priori unknown constant, which is the only general assumption imposed on it. Problems of this type often arise in applications. Two dimensionality reduction approaches to multidimensional optimization problems, i.e., the use of Peano curves (evolvents) and a recursive multistep scheme, are considered. A generalized scheme combining both approaches is proposed. In the new scheme, an original multidimensional problem is reduced to a family of lower-dimensional problems, which are solved using evolvents. An adaptive algorithm with the simultaneous solution of all resulting subproblems is implemented. Computational experiments on several hundred test problems are performed. In accordance with experimental evidence, the new dimensional reduction scheme is effective.

研究了多维多重极值优化问题及其求解的数值方法。目标函数应该以先验未知常数满足Lipschitz条件，这是对其施加的唯一一般假设。在应用中经常出现这种类型的问题。考虑了用于多维优化问题的二维降维方法，即使用Peano曲线（演化）和递归多步方案。提出了一种结合两种方法的通用方案。在新方案中，原始的多维问题被简化为一系列的低维问题，这些问题可以通过进化来解决。实现了同时解决所有子问题的自适应算法。对数百个测试问题进行了计算实验。根据实验证据，新的降维方案是有效的。