Abstract

Spherically constrained optimization, which minimizes an objective function on a unit sphere, has wide applications in numerical multilinear algebra, signal processing, solid mechanics, etc. In this paper, we consider a certain case that the derivatives of the objective function are unavailable. This case arises frequently in computational science, chemistry, physics, and other enormous areas. To explore the spherical structure of the above problem, we apply the Cayley transform to preserve iterates on the sphere and propose a derivative-free algorithm, which employs a simple model-based trust-region framework. Under mild conditions, global convergence of the proposed algorithm is established. Preliminary numerical experiments illustrate the promising performances of our algorithm.

中文翻译：

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球面约束优化的无导数算法

摘要

球面约束优化使单位球上的目标函数最小化，在数值多线性代数，信号处理，固体力学等方面具有广泛的应用。在本文中，我们考虑目标函数的导数不可用的特定情况。这种情况在计算科学，化学，物理和其他巨大领域中经常出现。为了探索上述问题的球面结构，我们应用Cayley变换在球面上保留迭代，并提出了无导数算法，该算法采用了基于模型的简单信任区域框架。在温和条件下，建立了该算法的全局收敛性。初步的数值实验说明了我们算法的有希望的性能。