Dr. Dennis AMELUNXEN

PhD – Universität Paderborn, Germany

Assistant Professor

Contact Information

Office:	G6613 Academic 1
Phone:	+852 3442-2178
Email:	damelunx@cityu.edu.hk
Web:	github

Research Interests

Computational Mathematics
Probabilistic Analyses
Convex and Integral Geometry
High-dimensional Geometry
Data Science

Dr Dennis Amelunxen received his PhD degree from Universität Paderborn, Germany, in 2011. Before joining City University in 2014, he worked as a postdoctoral fellow at Cornell University, USA, and at The University of Manchester, UK. His research interests include computational mathematics, geometric and probabilistic aspects of numerical algorithms, convex programming, and convex and integral geometry.

Award and Achievement

Aug 2015 “Information and Inference Best Paper Prize” Information and Inference: a Journal of the IMA. Best paper prize for "Living on the edge: phase transitions in convex programs with random data" by Dennis Amelunxen, Martin Lotz, Michael B. McCoy, and Joel A. Tropp . [Announcement]

Publication Show All Publications Show Prominent Publications

Journal

Amelunxen, D. & Lotz, M. (Aug 2017). Average-case complexity without the black swans. Journal of Complexity. 41. 82 - 101. doi:10.1016/j.jco.2016.12.002
Amelunxen, D. & Lotz, M. (2017). Intrinsic volumes of polyhedral cones: a combinatorial perspective. Discrete and Computational Geometry.
Amelunxen, D. , Lotz, M. , McCoy, M. B. & Tropp, J. A. (Apr 2014). Living on the edge: phase transitions in convex programs with random data. Information and Inference. 3(3). 224 - 294. doi:10.1093/imaiai/iau005
Amelunxen, D. & Bürgisser, P. (Jan 2014). Intrinsic volumes of symmetric cones and applications in convex programming. Mathematical Programming. 149(1). 105 - 130. doi:10.1007/s10107-013-0740-2
Amelunxen, D. & Bürgisser, P. (Nov 2013). Probabilistic Analysis of the Grassmann Condition Number. Foundations of Computational Mathematics. 15(1). 3 - 51. doi:10.1007/s10208-013-9178-4
Amelunxen, D. & Bürgisser, P. (Sep 2012). A Coordinate-Free Condition Number for Convex Programming. SIAM Journal on Optimization. 22(3). 1029 - 1041. doi:10.1137/110835177
Bürgisser, P. & Amelunxen, D. (Apr 2010). Robust smoothed analysis of a condition number for linear programming. Mathematical Programming. 131(1-2). 221 - 251. doi:10.1007/s10107-010-0346-x

Preprint

Amelunxen, D. (Dec 2014). Measures on polyhedral cones: characterizations and kinematic formulas.
arXiv:1412.1569 [math.MG]
Amelunxen, D. & Lotz, M. (Aug 2014). Gordon's inequality and condition numbers in conic optimization.
arXiv:1408.3016 [math.PR]

Unpublished

Amelunxen, D. & Bürgisser, P. (May 2012). Intrinsic volumes of symmetric cones.
arXiv:1205.1863 [math.OC]
This is an extended version of Intrinsic volumes of symmetric cones and applications in convex programming including an appendix on the biconic sigma algebra.

Software

Amelunxen, D. & Lotz, M. (Dec 2017). conivol: An R package for the (bivariate) chi-bar-squared distribution and conic intrinsic volumes.
source: github.com/damelunx/conivol
manual: damelunx.github.io/conivol
vignettes:
- Conic intrinsic volumes and (bivariate) chi-bar-squared distribution: introduces conic intrinsic volumes and (bivariate) chi-bar-squared distributions, as well as the computations involving polyhedral cones,
- Estimating conic intrinsic volumes from bivariate chi-bar-squared data: describes the details of the algorithm for finding the intrinsic volumes of closed convex cones from samples of the associated bivariate chi-bar-squared distribution,
- Bayesian estimates for conic intrinsic volumes: describes the Bayesian approach for reconstructing intrinsic volumes from sampling data, which can either be samples from the intrinsic volumes distribution (in the case of polyhedral cones), or from the bivariate chi-bar-squared distribution, and which can be with or without enforcing log-concavity of the intrinsic volumes.
Amelunxen, D. (Apr 2018). symconivol: An R package for intrinsic volumes and curvature measures of symmetric cones.
source: github.com/damelunx/symconivol
manual: damelunx.github.io/symconivol
vignette:
- Study on curvature measures of symmetric cones: analyzes the curvature measures of symmetric cones through the distribution of the Gaussian orthogonal/unitary/symplectic ensemble conditioned on the index function, that is, on the number of positive eigenvalues. Includes asymptotic estimates, limit curves, and finite-dimensional estimates. An estimator for the rank of the solution of a semidefinite program is derived.