Randomized methods bazed on new monte carlo schemes for convex optimization

Boris T. Polyak, Elena N. Gryazina

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

Abstract

We address randomized methods for convex optimization based on generating points uniformly distributed in a convex set. We estimate the rate of convergence for such methods and demonstrate the link with the center of gravity method. To implement such approach we exploit two modern Monte Carlo schemes for generating points which are approximately uniformly distributed in a given convex set. Both methods use boundary oracle to find an intersection of a ray and the set. The first method is Hit-and-Run, the second is sometimes called Shake-and-Bake. Numerical simulation results look very promising

Original languageEnglish
Title of host publication20th International Conference EURO Mini Conference "Continuous Optimization and Knowledge-Based Technologies", EurOPT 2008
EditorsLeonidas Sakalauskas, Gerhard-Wilhelm Weber, Edmundas Zavadskas
PublisherVilnius Gediminas Technical University
Pages485-489
Number of pages5
ISBN (Electronic)9789955282839
Publication statusPublished - 2008
Externally publishedYes
Event20th International Conference EURO Mini Conference: Continuous Optimization and Knowledge-Based Technologies, EurOPT 2008 - Neringa, Lithuania
Duration: 20 May 200823 May 2008

Publication series

Name20th International Conference EURO Mini Conference "Continuous Optimization and Knowledge-Based Technologies", EurOPT 2008

Conference

Conference20th International Conference EURO Mini Conference: Continuous Optimization and Knowledge-Based Technologies, EurOPT 2008
Country/TerritoryLithuania
CityNeringa
Period20/05/0823/05/08

Keywords

  • Hit-and-Run
  • Monte carlo
  • Optimization
  • Random search
  • Randomized algorithms
  • Shake-and-Bake

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