11 citations · 30 across the 3 of their papers we have counts for
10 papers
Effective Condition Number Bounds for Convex Regularization
Dennis Amelunxen, Martin Lotz, Jake Walvin
We derive bounds relating Renegar's condition number to quantities that govern the statistical performance of convex regularization in settings that include the -analysis s…
Average-case complexity without the black swans
Dennis Amelunxen, Martin Lotz
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 tra…
Intrinsic Volumes of Polyhedral Cones: A combinatorial perspective
Dennis Amelunxen, Martin Lotz
The theory of intrinsic volumes of convex cones has recently found striking applications in areas such as convex optimization and compressive sensing. This article provides a self-…
Measures on polyhedral cones: characterizations and kinematic formulas
Dennis Amelunxen
This paper is about conic intrinsic volumes and their associated integral geometry. We pay special attention to the biconic localizations of the conic intrinsic volumes, the so-cal…
Gordon's inequality and condition numbers in conic optimization
Dennis Amelunxen, Martin Lotz
The probabilistic analysis of condition numbers has traditionally been approached from different angles; one is based on Smale's program in complexity theory and features integral…
Living on the edge: Phase transitions in convex programs with random data
Dennis Amelunxen, Martin Lotz, Michael B. McCoy +1
Recent research indicates that many convex optimization problems with random constraints exhibit a phase transition as the number of constraints increases. For example, this phenom…