This article defines an efficient subspace method, called SSDFO, for unconstrained derivative-free optimization problems where the gradients of the objective function are Lipschitz continuous but only exact function values are available. SSDFO employs line searches along directions constructed on the basis of quadratic models. These approximate the objective function in a subspace spanned by some previous search directions. A worst-case complexity bound on the number of iterations and function evaluations is derived for a basic algorithm using this technique. Numerical results for a practical variant with additional heuristic features show that, on the unconstrained CUTEst test problems, SSDFO has superior performance compared to the best solvers from the literature.

本文定义了一种有效的子空间方法，称为 SSDFO，用于无约束无导数优化问题，其中目标函数的梯度是 Lipschitz 连续的，但只有精确的函数值可用。 SSDFO 采用沿基于二次模型构建的方向的线搜索。这些近似于由一些先前搜索方向跨越的子空间中的目标函数。使用这种技术的基本算法得出了迭代次数和函数评估的最坏情况复杂度界限。具有附加启发式特征的实际变体的数值结果表明，在无约束的 CUTEst 测试问题上，SSDFO 与文献中的最佳求解器相比具有更优越的性能。