Dimensionality reduction techniques for global optimization

Thesis

Though ubiquitous in applications, global optimisation problems are generally the most computationally intense due to their solution time growing exponentially with linear increase in their dimensions (this is the well known/so called ‘curse of dimensionality’). In this thesis, we show that this scalability — and sometimes even tractability — challenges can be overcome in the global optimization of functions with low effective dimensionality, that are constant along an (unknown) linear sub...

Expand abstract

Authors: Otemissov, A

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: dimensionality reduction techniques; functions with low effective dimensionality; unconstrained optimization; global optimization; random embeddings; constrained optimization
• Subjects: Stochastic processes; Dimension reduction (Statistics); Nonconvex programming; Mathematical optimization