Abstract
Manifold optimization is extremely relevant to problems of modern interest. This paper expands on iterative directional-search optimization frameworks for manifolds, to more general objects - orbifolds. The innovation is to tackle problems with discrete group structure, which apply to modernistic data models such as multisets, graphs, choice/voting data, hypercubes, crystagraphic structures, etc.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Absil, P.A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton (2008)
Jain, B., Obermayer, K.: Learning in Riemannian Orbifolds (2012) (preprint), http://arxiv.org/abs/1204.4294
Adem, A., Leida, J., Ruan, Y.: Orbifolds and Stringy Topology, 1st edn. Cambridge University Press, New York (2007)
Borzellino, J.E.: Riemannian Geometry of Orbifolds. Ph.D. thesis, UCLA (1992)
Tu, L.W.: An introduction to manifolds, 2nd edn. Springer (2011)
Bullo, F., Lewis, A.D.: Geometric Control of Mechanical Systems, 1st edn. Texts in Applied Mathematics, vol. 49. Springer, New York (2004)
Guerreiro, J.A.: Orbifolds and Wallpaper Patterns. Project Report (2009), http://www.math.ist.utl.pt/~rfern/advising#undergraduate
Arnold, L.A., Auger, A., Hansen, N., Ollivier, Y.: Information-Geometric Optimization Algorithms: A Unifying Picture via Invariance Principles. Tech. Report HAL-00601503 (2011), http://arxiv.org/abs/1106.3708
Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms, 3rd edn. Springer, New York (2007)
Göbel, M.: Computing bases for rings of permutation-invariant polynomials. Journal of Symbolic Computation 19, 285–291 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lim, F. (2013). On Directional-Search Procedures for Orbifolds: Connections with the Manifold Framework. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_63
Download citation
DOI: https://doi.org/10.1007/978-3-642-40020-9_63
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40019-3
Online ISBN: 978-3-642-40020-9
eBook Packages: Computer ScienceComputer Science (R0)