An iterative row-action method for interval convex programming

Y. Censor, A. Lent

Research output: Contribution to journalArticlepeer-review

Abstract

The iterative primal-dual method of Bregman for solving linearly constrained convex programming problems, which utilizes nonorthogonal projections onto hyperplanes, is represented in a compact form, and a complete proof of convergence is given for an almost cyclic control of the method. Based on this, a new algorithm for solving interval convex programming problems, i.e., problems of the form min f(x), subject to γ≤Ax≤δ, is proposed. For a certain family of functions f(x), which includes the norm ∥x∥ and the x log x entropy function, convergence is proved. The present row-action method is particularly suitable for handling problems in which the matrix A is large (or huge) and sparse.

Original languageEnglish
Pages (from-to)321-353
Number of pages33
JournalJournal of Optimization Theory and Applications
Volume34
Issue number3
DOIs
StatePublished - Jul 1981
Externally publishedYes

Keywords

  • entropy optimization
  • image reconstruction from projections
  • Interval convex programming
  • large and sparse matrices
  • nonorthogonal projections

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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