The Mehrotra predictor-corrector interior-point method as a perturbed composite Newton method

SIAM Journal on Optimization

Volumn 6, Issue 1, 1996, Pages 47-56

  Tapia, R ^a   Zhang, Y ^b   Saltzman, M ^c   Weiser, A ^a  

^a RICE UNIVERSITY   (United States)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^c CLEMSON UNIVERSITY   (United States)

Author keywords

Linear programming; Newton's method; Primal dual interior point algorithms

Indexed keywords

EID: 0030304769     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/0806004     Document Type: Article

References (16)

1. J. E. DENNIS, JR. AND R. B. SCHNABEL, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Englewood Cliffs, NJ, 1983. Russian edition, Mir Publishing Office, Moscow, 1988, O. Burdakov, translator.
2. A. EL-BAKRY, R. A. TAPIA, AND Y. ZHANG, A study of indicators for identifying zero variables in interior-point methods, SIAM Rev., 36 (1994), pp. 45-72.
3. M. KOJIMA, S. MIZUNO, AND A. YOSHISE, A primal-dual interior-point method for linear programming, in Progress in Mathematical Programming, Interior Point and Related Methods, N. Megiddo, ed., Springer-Verlag, New York, 1989, pp. 29-47.
4. I. J. LUSTIG, R. E. MARSTEN, AND D. F. SHANNO, On implementing Mehrotra's predictor-corrector interior point method for linear programming, Tech. Report SOR 90-03, Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ, April 1990.
5. N. MEGIDDO, Pathways to the optimal set in linear programming, in Progress in Mathematical Programming, Interior Point and Related Methods, N. Megiddo, ed., Springer-Verlag, New York, 1989, pp. 131-158.
6. S. MEHROTRA, On finding a vertex solution using interior-point methods, Tech. Report 89-22, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, 1989. Revised, January 1990.
7. _, On the implementation of a (primal-dual) interior point method, Tech. Report 90-03, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL, March 1990.
8. S. MIZUNO, M. J. TODD, AND Y. YE, Anticipated behavior of the path following algorithms for linear programming, Tech. Report No. 878, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, December 1989.
9. R. D. C. MONTEIRO, I. ADLER, AND M. G. C. RESENDE, A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension, ESRC Report 88-8, Department of Industrial Engineering and Operations Research, University of California, Berkeley, March 1988.
10. J. M. ORTEGA AND W. C. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
11. J. JI, F. POTRA, R. A. TAPIA, AND Y. ZHANG, An interior-point method with polynomial complexity and superlinear convergence for linear complementarity problems, TR91-23, Department of Computational and Applied Mathematics, Rice University, Houston, TX, July 1991. Submitted.
12. J. TRAUB, Iterative Methods for the Solution of Equations, Prentice Hall, Englewood Cliffs, NJ, 1964.
13. Y. ZHANG AND R. A. TAPIA, A superlinearly convergent polynomial primal-dual interior-point algorithm for linear programming, SIAM J. Optim., 3 (1993), pp. 118-133.
14. _, Superlinear and quadratic convergence of primal-dual interior-point algorithms for linear programming revisited, JOTA, 73 (1992), pp. 229-242.
15. Y. ZHANG, R. A. TAPIA, AND J. E. DENNIS, On the superlinear and quadratic convergence of primal-dual interior-point linear programming algorithms, SIAM J. Optim., 2 (1992), pp. 304-324.
16. Y. ZHANG, R. A. TAPIA, AND F. POTRA, On the superlinear convergence of interior-point algorithms for a general class of problems, SIAM J. Optim., 3 (1993), pp. 413-422.