A Flexible Framework for Cubic Regularization Algorithms for Nonconvex Optimization in Function Space

Abstract

We propose a cubic regularization algorithm that is constructed to deal with nonconvex minimization problems in function space. It allows for a flexible choice of the regularization term and thus accounts for the fact that in such problems one often has to deal with more than one norm. Global and local convergence results are established in a general framework.

Keywords:

• Non-convex optimization
• optimization in function space
• cubic regularization

AMS MSC 2000:

• 49M37
• 90C30