A large-step infeasible-interior-point method for the P*-matrix LCP

SIAM Journal on Optimization

Volumn 7, Issue 2, 1997, Pages 318-335

  Potra, Florian A ^a   Sheng, Rongqin ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Infeasible interior point algorithm; Linear complementarity problems; P* matrices; Polynomiality; Superlinear convergence

Indexed keywords

EID: 0031493116     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623495279359     Document Type: Article

References (22)

1. M. ANITESCU, G. LESAJA, AND F. A. POTRA, On the Equivalence Between Different Formulations and Algorithms for the P* (κ)-LCP, Reports on computational mathematics 71, Department of Mathematics, The University of Iowa, Iowa City, IA, June, 1995.
2. C. C. GONZAGA, The Largest Step Path Following Algorithm for Monotone Linear Complementary Problems, Technical reports, Delft Technical University, Delft, The Netherlands, January, 1993.
3. J. JI AND F. A. POTRA, An Infeasible-Interior-Point Method for the P*-Matrix LCP, Reports on computational mathematics 52, Department of Mathematics, The University of Iowa, Iowa City, IA, February, 1994.
4. J. JI, F. A. POTRA, AND R. SHENG, A predictor-corrector method for solving the P* (κ)-matrix LCP from infeasible starting points, Optim. Methods Software, 6 (1995), pp. 109-126.
5. M. KOJIMA, N. MEGIDDO, T. NOMA, AND A. YOSHISE, A unified approach to interior point algorithms for linear complementarity problems, Lecture Notes in Computer Science 538, Springer-Verlag, Berlin, New York, 1991.
6. S. MEHROTRA, Asymptotic Convergence in a Generalized-Predictor-Corrector Method, Technical report, Department of Industrial Engineering and Management Science, Northwestern University, Evanston, IL, October, 1992.
7. J. MIAO, A quadratically convergent O((1 + κ)√nL)-iteration algorithm for the P*(κ)-matrix linear complementarity problem, Math. Programming, 69 (1995), pp. 355-368.
8. S. MIZUNO, F. JARRE, AND J. STOER, A unified approach to infeasible-interior-point algorithms via geometrical linear complementarity problems, Appl. Math. Optim., 33 (1996), pp. 315-341.
9. J. M. ORTEGA AND W. C. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
10. F. A. POTRA, On Q-order and R-order of convergence, J. Optim. Theory Appl., 63 (1989), pp. 415-431.
11. F. A. POTRA, An O(nL) Infeasible-Interior-Point Algorithm for LCP with Quadratic Convergence, Reports on computational mathematics 50, Department of Mathematics, The University of Iowa, Iowa City, IA, January, 1994.
12. F. A. POTRA AND V. PTAK, Nondiscrete induction and iterative processes, Research Notes in Mathematics 103, Pitman, Boston, MA, 1984.
13. F. A. POTRA AND R. SHENG, Predictor-Corrector Algorithms for Solving P*(κ)-Matrix LCP from Arbitrary Positive Starting Points, Reports on computational mathematics 58, Department of Mathematics, The University of Iowa, Iowa City, IA, August 1994.
14. V. E. SHAMANSKII, On a modification of Newton's method, Ukrainian Math. J., 19 (1967), pp 133-138, (in Russian).
15. R. SHENG AND F. A. POTRA, A quadratically convergent infeasible-interior-point algorithm for LCP with polynomial complexity, SIAM J. Optim., 7 (1997), pp. 304-317.
16. J. F. TRAUB, Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, NJ, 1964.
17. S. J. WRIGHT, A path-following infeasible-interior-point algorithm for linear complementarity problems, Optim. Methods Software, 2 (1993), pp. 79-106.
18. S. J. WRIGHT, A path-following interior-point algorithm for linear and quadratic problems, Ann Oper. Res., 62 (1996), pp. 103-130.
19. S. J. WRIGHT, An infeasible-interior-point algorithm for linear complementarity problems, Math Programming, 67 (1994), pp. 29-52.
20. S. J. WRIGHT AND Y. ZHANG, A superquadratic infeasible-interior-point algorithm for linear complementarity problems, Math. Programming, 73 (1996), pp. 269-289.
21. X. XU, An O(√nL)-Iteration Large-Step Infeasible Path-Following Algorithm for Linear Programming, Department of Management Sciences, The University of Iowa, Iowa City, IA, August, 1994.
22. Y. ZHANG, On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem, SIAM J. Optim., 4 (1994), pp. 208-227.