Tensor methods for nonconvex optimization

Thesis

Traditionally, first-order gradient-based techniques and second-order Newton-type methods have dominated the field of optimization. In recent years, high-order tensor methods with regularization for nonconvex optimization have garnered significant research interest. These methods offer superior local convergence rates and improved worst-case evaluation complexity, where complexity is measured by the number of function and derivative evaluations (oracle calls) rather than by ...

Expand abstract

Authors: Zhu, KW

• DOI: 10.5287/ora-z6rxqeeo1
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: sum-of-squares techniques; higher-order optimization; regularization techniques; tractable polynomial optimization; computational complexity analysis; tensor method
• Subjects: Mathematics