No self-concordant barrier interior point method is strongly polynomial - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2022

No self-concordant barrier interior point method is strongly polynomial

Xavier Allamigeon
Stéphane Gaubert
Nicolas Vandame
  • Function : Author

Abstract

It is an open question to determine if the theory of self-concordant barriers can provide an interior point method with strongly polynomial complexity in linear programming. In the special case of the logarithmic barrier, it was shown in [Allamigeon, Benchimol, Gaubert and Joswig, SIAM J. on Applied Algebra and Geometry, 2018] that the answer is negative. In this paper, we show that none of the self-concordant barrier interior point methods is strongly polynomial. This result is obtained by establishing that, on parametric families of convex optimization problems, the log-limit of the central path degenerates to a piecewise linear curve, independently of the choice of the barrier function. We provide an explicit linear program that falls in the same class as the Klee–Minty counterexample for the simplex method, i.e., in which the feasible region is a combinatorial cube and the number of iterations is Ω(2n).

Dates and versions

hal-03915670 , version 1 (29-12-2022)

Identifiers

Cite

Xavier Allamigeon, Stéphane Gaubert, Nicolas Vandame. No self-concordant barrier interior point method is strongly polynomial. STOC 2022 - 54th Annual ACM SIGACT Symposium on Theory of Computing, Jun 2022, Rome, Italy. pp.515-528, ⟨10.1145/3519935.3519997⟩. ⟨hal-03915670⟩
21 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More