Random projection algorithms for convex set intersection problems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

15 Citations (Scopus)

Abstract

The focus of this paper is on the set intersection problem for closed convex sets admitting projection operation in a closed form. The objective is to investigate algorithms that would converge (in some sense) if and only if the problem has a solution. To do so, we view the set intersection problem as a stochastic optimization problem of minimizing the "average" residual error of the set collection. We consider a stochastic gradient method as a main tool for investigating the properties of the stochastic optimization problem. We show that the stochastic optimization problem has a solution if and only if the stochastic gradient method is convergent almost surely. We then consider a special case of the method, namely the random projection method, and we analyze its convergence. We show that a solution of the intersection problem exists if and only if the random projection method exhibits certain convergence behavior almost surely. In addition, we provide convergence rate results for the expected residual error.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages7655-7660
Number of pages6
DOIs
StatePublished - 2010
Externally publishedYes
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Fingerprint

Random Projection
Projection Algorithm
Convex Sets
Stochastic Optimization
Gradient methods
Intersection
Stochastic Gradient
Stochastic Methods
Gradient Method
If and only if
Optimization Problem
Projection Method
Closed set
Convergence Rate
Closed-form
Projection
Converge

Keywords

  • Convex sets
  • Intersection problem
  • Random projection

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Nedich, A. (2010). Random projection algorithms for convex set intersection problems. In 2010 49th IEEE Conference on Decision and Control, CDC 2010 (pp. 7655-7660). [5717734] https://doi.org/10.1109/CDC.2010.5717734

Random projection algorithms for convex set intersection problems. / Nedich, Angelia.

2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 7655-7660 5717734.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Nedich, A 2010, Random projection algorithms for convex set intersection problems. in 2010 49th IEEE Conference on Decision and Control, CDC 2010., 5717734, pp. 7655-7660, 2010 49th IEEE Conference on Decision and Control, CDC 2010, Atlanta, GA, United States, 12/15/10. https://doi.org/10.1109/CDC.2010.5717734
Nedich A. Random projection algorithms for convex set intersection problems. In 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. p. 7655-7660. 5717734 https://doi.org/10.1109/CDC.2010.5717734
Nedich, Angelia. / Random projection algorithms for convex set intersection problems. 2010 49th IEEE Conference on Decision and Control, CDC 2010. 2010. pp. 7655-7660
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