Spectral operators of matrices
MetadataShow full item record
The class of matrix optimization problems (MOPs) has been recognized in recent years to be a powerful tool to model many important applications involving structured low rank matrices within and beyond the optimization community. This trend can be credited to some extent to the exciting developments in emerging fields such as compressed sensing. The Löwner operator, which generates a matrix valued function via applying a single-variable function to each of the singular values of a matrix, has played an important role for a long time in solving matrix optimization problems. However, the classical theory developed for the Löwner operator has become inadequate in these recent applications. The main objective of this paper is to provide necessary theoretical foundations from the perspectives of designing efficient numerical methods for solving MOPs. We achieve this goal by introducing and conducting a thorough study on a new class of matrix valued functions, coined as spectral operators of matrices. Several fundamental properties of spectral operators, including the well-definedness, continuity, directional differentiability and Fréchet-differentiability are systematically studied. © 2017 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10107-017-1162-3
Showing items related by title, author, creator and subject.
Zhou, Jingyang (2011)In this thesis, we deal with several optimal guidance and control problems of the spacecrafts arising from the study of lunar exploration. The research is composed of three parts: 1. Optimal guidance for the lunar module ...
Ferrante, A.; Ntogramatzidis, Lorenzo (2017)Three hundred years have passed since Jacopo Francesco Riccati analyzed a quadratic differential equation that would have been of crucial importance in many fields of engineering and applied mathematics. Indeed, countless ...
Identification of the dynamic behaviour of an autogenous mill by use of time series cluster analysisBardinas, J.; Aldrich, Chris; Albijanic, Boris (2016)© 2016 TAPPI Press. All rights reserved. The use of autogenous mills has become widespread, owing to their capacity and favorable capital and operating costs. Optimal operation of these systems is critical, given their ...