Convergence of the cyclical relaxation method for linear inequalities

1. S. Agmon, “The relaxation method for linear inequalities”,Canadian Journal of Mathematics 6 (1954) 382–392.

   MATH  MathSciNet  Google Scholar 

2. Y. Censor, P.P.B. Eggermont and D. Gordon “Strong underrelaxation in Kaczmarz's method for inconsistent systems”, Technical Report MIPG62, Department of Radiology, University of Pennsylvania, Philadelphia, PA, December, 1981.

   Google Scholar 

3. R.W. Cottle and J.-S. Pang, “On solving linear complementarity problems as linear programs”,Mathematical Programming Study 7 (1978) 88–107.

   MATH  MathSciNet  Google Scholar 

4. J.L. Goffin, “On the nonpolynomiality of the relaxation method for systems of linear inequalities”,Mathematical Programming 22 (1982) 93–103.

   Article  MATH  MathSciNet  Google Scholar 

5. J.L. Goffin, “Acceleration in the relaxation method for linear inequalities and subgradient optimization”, in: E.A. Nurminski, ed., Progress in Nondifferentiable Optimization (IIASA, Laxenburg, 1982) pp. 29–59.

   Google Scholar 

6. J.L. Goffin, “The relaxation method for solving system of linear inequalities”,Mathematics of Operations Research 5 (1980) 388–414.

   Article  MATH  MathSciNet  Google Scholar 

7. G.T. herman,Image reconstructions from projections, the fundamentals of computerized tomography (Academic Press, New York, 1980).

   Google Scholar 

8. G.T. Herman, “A relaxation method for reconstructing objects from noisy X-rays”,Mathematical Programming 8 (1975) 1–19.

   Article  MATH  MathSciNet  Google Scholar 

9. A.S. Householder and F.L. Bauer, “On certain iterative methods for solving linear systems”,Numerische Mathematik 2 (1960) 55–59.

   Article  MATH  MathSciNet  Google Scholar 

10. L.G. Khachian, “A polynomial algorithm in linear programming”,Doklady Akademii Nauk SSSR 244 (1979) 1093–1095 [translated inSoviet Mathematics Doklady 20 (1979) 191–194].

    MathSciNet  Google Scholar 

11. Th. Motzkin and I.J. Schoenberg, “The relaxation method for linear inequalities”,Canadian Journal of Mathematics 6 (1954) 393–404.

    MATH  MathSciNet  Google Scholar 

12. W. Oettli, “An iterative method, having a linear rate of convergence, for solving a pair of dual linear programs”,Mathematical Programming 3 (1972) 302–311.

    Article  MATH  MathSciNet  Google Scholar 

13. M.J. Todd, “Some results on the relaxation methods for linear inequalities”, Technical Report 419, SORIE Cornell University, Ithaca, NY, April, 1979.

    Google Scholar 

Download references