Random projections are used as dimensional reduction techniques in many situations. They project a set of points in a high dimensional space to a lower dimensional one while approximately preserving all pairwise Euclidean distances. Usually, random projections are applied to numerical data. In this paper, however, we present a successful application of random projections to quadratic programming problems subject to polyhedral and a Euclidean ball constraint. We derive approximate feasibility and optimality results for the lower dimensional problem. We then show the practical usefulness of this idea on many random instances, as well as on two portfolio optimization instances with over 25M nonzeros in the (quadratic) risk term.
CITATION STYLE
Vu, K., Poirion, P. L., D’Ambrosio, C., & Liberti, L. (2019). Random Projections for Quadratic Programs over a Euclidean Ball. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11480 LNCS, pp. 442–452). Springer Verlag. https://doi.org/10.1007/978-3-030-17953-3_33
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