We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is obtained through minimization in the full/high-resolution space, ensuring global convergence to a critical point. The second search direction is obtained through minimization in the randomly generated subspace, which, in turn, allows for convergence acceleration. The efficiency of the proposed TLTR method is demonstrated through numerical experiments in the field of machine learning

翻译：本文提出一种用于求解无约束非线性优化问题的双层信赖域方法（TLTR）。该方法采用基于两个不同搜索方向的复合迭代步。第一个搜索方向通过在完整/高分辨率空间中进行最小化获得，确保算法全局收敛至临界点。第二个搜索方向通过在随机生成的子空间中进行最小化获得，从而实现收敛加速。通过在机器学习领域的数值实验，验证了所提TLTR方法的有效性。