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ABS Methods to Solve Optimization Problems: A Review

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Author Affiliations

  • 1Department of Mathematics, Government Engineering College Ajmer, INDIA
  • 2Department of Computer Science, Sanskriti Computer Education College, Beawar, INDIA

Res. J. Mathematical & Statistical Sci., Volume 1, Issue (2), Pages 19-21, March,12 (2013)

Abstract

The ABS methods have been studied a lot in last few years. The ABS methods have been used broadly for solving linear and nonlinear system of equations comprising large number of constraints and variables. This work gives a review of the work done by earlier researchers to apply ABS algorithm for different kind of optimization problems i.e.; for solving determined or undetermined linear systems, linear least squares optimization problem and integer equation and linear programming etc. AMS Subject Classification: 65F30

References

  1. Bodon Elena, Numerical experiments with Gauss-ABS algorithms on tridiagonal systems of linear equations, QDMSIA, 31 (1992)
  2. Xia Zunquan, ABS reformulation of some versions of the simplex method for linear programming Q MSIA, 10 (1995)
  3. Feng E., Wang X. and Wang X.L, On the application of the ABS algorithm to linear programming and linear complementarity, OMS, 8, 133-142 (1997)
  4. Gabriela Kalnova, Pivoting algorithm in class of ABS methods Archivum Mathematicum (BRNO), Tomus 32, 167-180 (1996)
  5. Xia Zunquan, ABD derivation of affine-type projection for interior point methods via the ABS algorithm, QDMSIA 35 (1996)
  6. Adib Majid, Mahdavi-Amiri Nezam and Spedicato Emilio, ABS type methods for solving m linear equations in m/2 steps, QDMSIA, 8 (2000)
  7. Esmaeili Hamid, Mahdavi-Amiri and Spedicato Emilio, ABS solution of a class of linear integer inequalities and integer LPproblems QDMSIA, 3 (2001)
  8. Bodon Elena, Luskan Ladislav and Spedicato Emilio, Computational experiments with conjugate type ABS algorithms QDMSIA, 26 (2001)
  9. Esmaeili Hamid, Mahdavi-Amiri Nezam and Spedicato Emilio, A class of ABS algorithm for Diophantine linear systems, Numer.Math., 90, 101-115 (2001)
  10. Bodon Elena, ABS codes for banded linear determined and undetermined systems QDMSIA, 9 (2001)
  11. Spedicato Emilio and Bodon Elena, Numerical experiments of the ABS algorithm with iterative refinement on linear least squaresproblem QDMSIA, 7 (2002)
  12. Bodon Elena, ABS codes for linear least squares, QDMSIA, 3 (2002)
  13. Spedicato Emilio, Li-Ping Pang, Xia Zun- Quan and Wang Wei, A method for solving linear inequality system QDMSIA, 19 (2004)
  14. Spedicato Emilio, Xia Zun-Quan and Zhang Li- Wei, Application of the integer ABS algorithms to integer nonlinear optimization,QDMSIA, 18 (2004), undefined
  15. Esmaeili Hamid, Mahdavi-Amiri ,Nezam and Spedicato Emilio, Explicit ABS solution of a class of linear inequality system and LPproblems, Bulletin of the Iranian Mathematical Society, 30(2), 21-38 (2004)
  16. Xia Zun-Quan and Zou Mei-Feng, ABS algorithm for Diophantine linear equations and integer LP problems, QDMSIA, 3 (2004)
  17. Amini Keyvan, Solving rank one revised linear system by the scaled ABS method, ANZIAM J., 46, 225-236 (2004)
  18. Guo Qiang and Liu Jian-Guo, An two phase ABS method for solving over determined system of linear inequalities, J. Appl. Math. &Computing, 21(1-2), 259-267 (2006)
  19. Galantai A. and Spedicato E., ABS methods for nonlinear systems of algebraic equations, (2007)
  20. Emilio Spedicato and Marco Bonomi, Application of ABS methods to the primal-dual interior point method for linear programming, QDMSIA, 6 (2007)
  21. Gao Cheng-Zhi and Dong Yu-Lin, ABS algorithm for solving a class of linear Diophantine inequalities and integer LP problems, J.Appl. Math. & Informatics, 26(1-2), 349-353 (2008)
  22. Spedicato Emilio, Bodon Elena, Xia Zunquan and Mahdavi-Amiri Nezam, ABS methods for continuous and integer linear equationsand optimization, CEJOR, 18, 73-95 (2010)
  23. Khorramizadeh Mostafa, On solving newton systems of primal-dual infeasible interior point methods using ABS methods, AppliedMathematical Sciences, 6(106), 5263-5272 (2012)