Random projections for conic programs

Leo Liberti (1) , Pierre-Louis Poirion (2) , Ky Vu (3)

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

We discuss the application of random projections to conic programming: notably linear, second-order and semidefinite programs. We prove general approximation results on feasibility and optimality using the framework of formally real Jordan algebras. We then discuss some computational experiments on randomly generated semidefinite programs in order to illustrate the practical applicability of our ideas.

Mots clés: Mathematical Programming; Approximation; Johnson-Lindenstrauss Lemma; Jordan algebra

Domaines: Recherche opérationnelle [math.OC]; Algèbre commutative [math.AC]

Leo Liberti, Pierre-Louis Poirion, Ky Vu. Random projections for conic programs. Linear Algebra and its Applications, 2021, 626, pp.204-220. ⟨10.1016/j.laa.2021.06.010⟩. ⟨hal-03318771⟩