Hit-and-Run: Randomized technique for control problems recasted as concave programming

B. T. Polyak, E. N. Gryazina

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Citations (Scopus)


It is known that many challenging problems in control theory belong to the class of the minimization of a concave function over convex constraints. These are, for instance, static output feedback and robust fixed order control. We propose new randomized algorithm for these problems as a reasonable alternative for global optimization techniques. The method consists of two steps: first, we generate asymptotically uniform random samples in a convex domain via Hit-and-Run method and then apply local descent procedure based on conditional gradient for a concave function treating samples as starting points. Due to the diversity of the samples we obtain that the portion of successful descents is large enough. Simulations for the problem of stabilization of the inverted pendulum confirm the efficiency of the proposed algorithm.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages5
Edition1 PART 1
ISBN (Print)9783902661937
Publication statusPublished - 2011
Externally publishedYes

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670


  • Design
  • Global optimization
  • Hit-and-Run
  • Linear systems
  • Randomized methods
  • Stabilization


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