An interior points algorithm for the convex feasibility problem

Ron Aharoni, Abraham Berman, Yair Censor

Research output: Contribution to journalArticlepeer-review


The problem of finding a point in the intersection of a finite family of convex sets in the Euclidean space R″ is considered here. We present a general algorithmic scheme which employs projections onto separating hyperplanes instead of projections onto the convex sets. This scheme includes the method of successive projections of Gubin et al., USSR Comp. Math. and Math. Phys. 7 (1967), 1-24, as a special case. A different realization proposed here is capable of handling the problem when the sets are solid and an interior point of each set is available. This alternative algorithm may, in certain cases, be more attractive than the method of Gubin et al.

Original languageEnglish
Pages (from-to)479-489
Number of pages11
JournalAdvances in Applied Mathematics
Issue number4
StatePublished - Dec 1983

ASJC Scopus subject areas

  • Applied Mathematics


Dive into the research topics of 'An interior points algorithm for the convex feasibility problem'. Together they form a unique fingerprint.

Cite this