Abstract

A modification of Polyak’s special method of convex optimization is proposed. The properties of the corresponding algorithm are studied by computational experiments for convex separable and nonseparable optimization problems, nonconvex optimization problems for the potentials of atomic-molecular clusters, and a model optimal control problem. Sequential and parallel versions of the algorithm have been implemented, which made it possible to solve problems with dimensions of up to one hundred billion variables.

中文翻译：

---

使用 Polyak 方法改进的高维优化问题的数值研究

摘要

提出了对 Polyak 的特殊凸优化方法的改进。通过凸可分离和不可分离优化问题、原子分子簇势的非凸优化问题和模型最优控制问题的计算实验研究了相应算法的性质。已经实现了该算法的顺序和并行版本，这使得解决高达 1000 亿个变量的问题成为可能。