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Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenon emerges in theâ€¦ (More)

- Dennis Amelunxen, Martin Lotz, Michael B. McCoy, Joel A. Tropp
- ArXiv
- 2013

Recent empirical research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenomenonâ€¦ (More)

- Dennis Amelunxen, Peter BÃ¼rgisser
- SIAM Journal on Optimization
- 2012

We introduce and analyze a natural geometric version of Renegarâ€™s condition numberR for the homogeneous convex feasibility problem associated with a regular cone C âŠ† R. Let Grn,m denote the Grassmannâ€¦ (More)

- Dennis Amelunxen
- 2011

The focus of this paper is the homogeneous convex feasibility problem, which is the following question: Given an m-dimensional subspace of R, does this subspace intersect a fixed convex cone solelyâ€¦ (More)

- Dennis Amelunxen, Martin Lotz
- J. Complexity
- 2017

We introduce the concept of weak average-case analysis as an attempt to achieve theoretical complexity results that are closer to practical experience than those resulting from traditionalâ€¦ (More)

- Dennis Amelunxen, Peter BÃ¼rgisser
- Foundations of Computational Mathematics
- 2015

We perform an average analysis of the Grassmann condition number C (A) for the homogeneous convex feasibility problem âˆƒx âˆˆ C \ 0 : Ax = 0, where C âŠ‚ R may be any regular cone. This in particularâ€¦ (More)

- Dennis Amelunxen, Peter BÃ¼rgisser
- Math. Program.
- 2015

We express the probability distribution of the solution of a random (standard Gaussian) instance of a convex cone program in terms of the intrinsic volumes and curvature measures of the referenceâ€¦ (More)

- Peter BÃ¼rgisser, Dennis Amelunxen
- Math. Program.
- 2012

We perform a smoothed analysis of the GCC-condition number C (A) of the linear programming feasibility problem âˆƒx âˆˆ R Ax < 0. Suppose that Ä€ is any matrix with rows ai of euclidean norm 1 and,â€¦ (More)

- Dennis Amelunxen, Martin Lotz
- Discrete & Computational Geometry
- 2017

These notes provide a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones. Streamlined derivations of the General Steiner formula, the conic analogues of theâ€¦ (More)

We compute the intrinsic volumes of the cone of positive semidefinite matrices over the real numbers, over the complex numbers, and over the quaternions, in terms of integrals related to Mehtaâ€™sâ€¦ (More)