Solving linear feasibility in linear number of steps with self-concordant Perceptron.

Adrien Chan-Hon-Tong (1)

1 DTIS, ONERA, Université Paris Saclay [Palaiseau]

This paper offers an algorithms which solves any linear feasibility instance with a number of step which is at most linear in the binary size of the instance. This algorithm combines Perceptron and self concordant functions (log barrier) features. In particular, algorithm step are damped Newton step mainly consisting in solving a set of linear equations. Using common conversion, this algorithm could be used to solve linear programming, but, this leads to a slightly higher time complexity than state of the art. Inversely, times complexity for linear separability is state of the art, and, binary complexity is also mastered thank to a specific rounding process.

Mots clés: Linear programming; log barrier; polynomial times

Domaines: Recherche opérationnelle [math.OC]

Adrien Chan-Hon-Tong. Solving linear feasibility in linear number of steps with self-concordant Perceptron.. 2020. ⟨hal-00722920v31⟩