Papers › Geometry of quadratic maps via convex relaxation
Geometry of quadratic maps via convex relaxation
Anatoly Dymarsky, Elena Gryazina, Sergei Volodin, Boris Polyak
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex. Remarkably, even when the image is not convex it often exhibits hidden convexity: a surprising efficiency of convex relaxation to address various geometric questions by reformulating them in terms of convex optimization problems. In this paper we employ this strategy and put forward several algorithms that solve the following problems pertaining to the image: verify if a given point does not belong to the image; find the boundary point of the image lying in a particular direction; stochastically check if the image is convex, and if it is not, find a maximal convex subset of the image. Proposed algorithms are implemented in the form of an open-source MATLAB library CAQM, which accompanies the paper. Our results can be used for various problems of discrete optimization, uncertainty analysis, physical applications, and study of power flow equations.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections