On the identification of zero variables in an interior-point framework

SIAM Journal on Optimization

Volumn 10, Issue 4, 2000, Pages 1058-1078

  Facchinei, Francisco ^a   Fischer, Andreas ^b   Kanzow, Christian ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b TU DORTMUND UNIVERSITY   (Germany)

^c UNIVERSITY OF HAMBURG   (Germany)

Author keywords

Column sufficient matrix; Growth function; Identification of zero variables; Indicator function; Interior point method; Linear complementarity problem

Indexed keywords

EID: 0034345413     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623498339739     Document Type: Article

References (23)

1. R. W. COTTLE, J.-S. PANG, AND R. E. STONE, The Linear Complementarity Problem, Academic Press, Boston, 1992.
2. R. W. COTTLE, J.-S. PANG, AND V. VENKATESWARAN, Sufficient matrices and the linear complementarity problem, Linear Algebra Appl., 114/115 (1989), pp. 231-249.
3. A. S. 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.
4. A. S. EL-BAKRY, R. A. TAPIA, AND Y. ZHANG, On the convergence rate of Newton interior-point methods in the absence of strict complementarity, Comput. Optim. Appl., 6 (1996), pp. 157-167.
5. F. FACCHINEI, A. FISCHER, AND C. KANZOW, On the accurate identification of active constraints, SIAM J. Optim., 9 (1998), pp. 14-32.
6. F. FACCHINEI, A. FISCHER, AND C. KANZOW, On the Identification of Zero Variables in an Interior-Point Framework: Complete Numerical Results, Mathematical Programming Technical Report 98-05-results, Computer Sciences Department, University of Wisconsin-Madison, Madison, WI, 1998; also available online from http://www.math.uni-hamburg.de/home/kanzow, http://www-lsx.mathematik.uni-dortmund.de/user/lsx/fischer, and http://dis.uniromal.it/~facchinei.
7. A. J. GOLDMAN AND A. W. TUCKER, Theory of linear programming, in Linear Inequalities and Related Systems, H. W. Kuhn and A. W. Tucker, eds., Princeton University Press, Princeton, NJ, 1966, pp. 53-97.
8. W. HOCK AND K. SCHITTKOWSKI, Test Examples for Nonlinear Programming Codes, Lecture Notes in Econom. and Math. Systems 187, Springer-Verlag, Berlin, Germany, 1981.
9. J. JI AND F. POTRA, Tapia indicators and finite termination of infeasible-interior-point methods for degenerate LCP, in Mathematics of Numerical Analysis, Lectures in Appl. Math. 32, J. Renegar, M. Shub, and S. Smale, eds., AMS, Providence, RI, 1996, pp. 443-454.
10. C. KANZOW AND M. FUKUSHIMA, Equivalence of the generalized complementarity problem to differentiable unconstrained minimization, J. Optim. Theory Appl., 90 (1996), pp. 581-603.
11. Z.-Q. LUO AND P. TSENG, Error bound and convergence analysis of matrix splitting algorithms for the affine variational inequality problem, SIAM J. Optim., 2 (1992), pp. 43-54.
12. O. L. MANGASARIAN, Error bounds for nondegenerate monotone linear complementarity problems, Math. Programming, 48 (1990), pp. 437-445.
13. O. L. MANGASARIAN AND T.-H. SHIAU, Error bounds for monotone linear complementarity problems, Math. Programming, 36 (1986), pp. 81-89.
14. R. D. C. MONTEIRO AND S. J. WRIGHT, Local convergence of interior-point algorithms for degenerate monotone LCP, Comput. Optim. Appl., 3 (1994), pp. 131-155.
15. J.-S. PANG, Error bounds in mathematical programming, Math. Programming, 79 (1997), pp. 299-332.
16. F. A. POTRA AND R. SHENG, A superlinearly convergent infeasible-interior-point algorithm for degenerate LCP, J. Optim. Theory Appl., 97 (1998), pp. 249-269.
17. C. ROOS, T. TERLAKY, AND J.-PH. VIAL, Theory and Algorithms for Linear Optimization: An Interior Point Approach, John Wiley, Chichester, UK, 1997.
18. R. A. TAPIA, On the role of slack variables in quasi-Newton methods for constrained optimization, in Numerical Optimization of Dynamic Systems, L. W. C. Dixon and G. P. Szego, eds., North-Holland, Amsterdam, 1980, pp. 235-246.
19. P. TSENG, Growth behaviour of a class of merit functions for the nonlinear complementarity problem, J. Optim. Theory Appl., 89 (1996), pp. 17-37.
20. S. J. WRIGHT, Primal-Dual Interior-Point Methods, SIAM, Philadelphia, 1996.
21. Y. YE, Interior Point Algorithms: Theory and Analysis, John Wiley, New York, 1997.
22. Y. ZHANG, User's guide to LIPSOL: Linear programming interior point solvers, version 0.4, Optim. Methods Softw., 12 (1999), pp. 385-396.
23. Y. ZHANG, Solving large-scale linear programs by interior-point methods under the MATLAB environment, Optim. Methods Softw., 10 (1998), pp. 1-31.