On the convergence rate of newton interior-point methods in the absence of strict complementarity

Computational Optimization and Applications

Volumn 6, Issue 2, 1996, Pages 157-167

  El Bakry, A S ^a,b   Tapia, R A ^c   Zhang, Y ^b,d  

^a Alexandria University Faculty Of Science   (Egypt)

^b RICE UNIVERSITY   (United States)

^c Rice University   (United States)

^d UNIVERSITY OF MARYLAND   (United States)

Author keywords

Interior point methods; Linear convergence; Q1 factors; Strict complementarity; The Tapia indicators

Indexed keywords

COMPUTATIONAL METHODS; ITERATIVE METHODS; OPTIMIZATION; PROBLEM SOLVING;

CONVERGENCE RATE; LINEAR COMPLEMENTARITY PROBLEMS; NEWTON INTERIOR POINT METHODS; TAPIA INDICATORS;

CONVERGENCE OF NUMERICAL METHODS;

EID: 0030242534     PISSN: 09266003     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00249644     Document Type: Article

References (10)

1. A.S. El-Bakry, "On the role of indicators in identifying zero variables in linear programming," Ph.D. Thesis, Department of Mathematical Sciences, Rice University, Houston, Texas 77251, 1991.
2. A.S. El-Bakry, R.A. Tapia, and Y. Zhang, "A study of indicators for identifying zero variables in interior-point methods," SIAM Review, vol. 36, pp. 45-72, 1994.
3. A.J. Goldman and A.W. Tucker, "Theory of linear programming," in H.W. Kuhn and A.W. Tucker (Eds.), Linear Inequalities and Related Systems, Princeton University Press, 1956, pp. 53-97.
4. O. Güler and Y. Ye, "Convergence behavior of some interior-point algorithms," Math. Programming, Series A, vol. 60, pp. 215-228, 1993.
5. W. Hock and K. Schittkowski, Test Examples for Nonlinear Programming Codes, Springer-Verlag, New York, 1981.
6. S. Mizuno, "A superlinearly convergent infeasible interior-point algorithm for geometric LCPs without a strictly complementary solution," Technical Report 878, School of Operations Research and Industrial Engineering, Cornell University, 1994.
7. R.C. Monteiro and S. Wright, "Local convergence of interior-point algorithms for degenerate monotone LCP problems," Computational Optimization and Applications, vol. 3, pp. 131-155, 1994.
8. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
9. F.A. Potra and R. Sheng, "A superlinearly convergent infeasible interior-point algorithm for degenerate LCP," Technical Report 66, Department of Mathematics, Iowa University, Iowa 52242, 1995.
10. 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. on Optimization, vol. 2, pp. 304-324, 1992.