Dr. Pierre-Louis POIRION (Mathematical and Algorithmic Science Lab at Huawei Technologies France, France)
Random projections for symmetric cone programming
The well-known Johnson-Lindenstrauss lemma states that there are random matrices with surprisingly few rows that approximately preserve pairwise Euclidean distances among a set of points. In this talk, we exploit this result to prove that one can approximately solve, with a probabilistic algorithm, a Symmetric Cone Program with a large set of equality constraints by solving a projected version having a much smaller set of constraints.
We will more particularly study the LP case and show that our algorithm can solve large randomly generated LP instances.