Superlinearly convergent infeasible-interior-point algorithm for degenerate LCP

Journal of Optimization Theory and Applications

Volumn 97, Issue 2, 1998, Pages 249-269

  Potra, F A ^a   Sheng, R ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

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

Indexed keywords

FACTORIZATION; ITERATIVE METHODS; MATRIX ALGEBRA;

INFEASIBLE PATHS; INFEASIBLE-INTERIOR-POINT ALGORITHM; INTERIOR POINT ALGORITHM; LINEAR COMPLEMENTARITY PROBLEMS; P-MATRICES; P-MATRIX; PATH-FOLLOWING ALGORITHM; POLYNOMIALITY; SUFFICIENT MATRIX; SUPERLINEAR CONVERGENCE;

COMPUTATIONAL COMPLEXITY;

EID: 0041193084     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022670415661     Document Type: Article

References (15)

1. COTTLE, R. W., PANG, J. S., and VENKATESWARAN, V., Sufficient Matrices and the Linear Complementarity Problem, Linear Algebra and Its Applications, Vol. 114/115, pp. 231-249, 1989.
2. VÄLIAHO, H., P*-Matrices Are Just Sufficient, Linear Algebra and Its Applications, Vol. 239, pp. 103-108, 1996.
3. KOJIMA, M., MEGIDDO, N., NOMA, T., and YOSHISE, A., A Unified Approach to Interior-Point Algorithms for Linear Complementarity Problems, Lecture Notes in Computer Science, Vol. 538, 1991.
4. 0, Linear Algebra and Its Applications, Vol. 223/224, pp. 325-335, 1995.
5. MIAO, J., A Quadratically Convergent O(( 1 + κ)κnL)-Iteration Algorithm for the P*(κ)-Matrix Linear Complementarity Problem, Mathematical Programming, Vol. 69, pp. 355-368, 1995.
6. MIZUNO, S., TODD, M. J., and YE, Y., On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming, Mathematics of Operations Research, Vol. 18, pp. 964-981, 1993.
7. JI, J., and POTRA, F. A., An Infeasible-Interior-Point Method for the P*-Matrix LCP, Computational Mathematics Report 52, Department of Mathematics, University of Iowa, Iowa City, Iowa, 1994.
8. JI, J., POTRA, F. A., and SHENG, R., A Predictor-Corrector Method for Solving the P*(κ)-Matrix LCP from Infeasible Starting Points, Optimization Methods and Software. Vol. 6, pp. 109-126, 1995.
9. POTRA, F. A., and SHENG, R., Predictor-Corrector Algorithms for Solving P*(κ)-Matrix LCP from Arbitrary Positive Starting Points, Mathematical Programming, Vol. 76, pp. 223-244, 1997.
10. POTRA, F. A , and SHENG, R., A Large-Step Infeasible-Interior-Point Method for the P*-Matrix LCP, SIAM Journal on Optimization, Vol. 72, pp. 318-335, 1997.
11. MONTEIRO, R. D. C., and WRIGHT, S. J., Local Convergence of Interior-Point Algorithms for Degenerate Monotone LCP, Computational Optimization and Applications, Vol. 3, pp 131-155, 1993.
12. YE, Y., and ANSTREICHER, K., On Quadratic and O(√nL) Convergence of Predictor-Corrector Algorithm for LCP, Mathematical Programming, Vol. 62, pp. 537-551, 1993.
13. MIZUNO, S., A Superlinearly Convergent Infeasible-Interior-Point Algorithm for Geometrical LCPs without a Strictly Complementary Condition, Mathematics of Operations Research, Vol. 21, pp. 382-400, 1996.
14. WRIGHT, S. J., A Path-Following Interior-Point Algorithm for Linear and Quadratic Problems, Preprint MCS-P401-1293, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Illinois, 1993.
15. POTRA, F. A., On Q-Order and R-Order of Convergence, Journal of Optimization Theory and Applications, Vol. 63, pp. 415-431, 1989.