Random Projections for Quadratic Programs over a Euclidean Ball

Ky Vu , Pierre-Louis Poirion (1) , Claudia d'Ambrosio (2) , Leo Liberti (2)

1 RIKEN AIP - RIKEN Center for Advanced Intelligence Project [Tokyo]
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

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.

Domaines: Recherche opérationnelle [math.OC]; Optimisation et contrôle [math.OC]

Ky Vu, Pierre-Louis Poirion, Claudia d'Ambrosio, Leo Liberti. Random Projections for Quadratic Programs over a Euclidean Ball. Integer Programming and Combinatorial Optimization (IPCO), 2019, Ann Arbor, United States. pp.442-452, ⟨10.1007/978-3-030-17953-3_33⟩. ⟨hal-02869206⟩