메뉴 건너뛰기




Volumn 102, Issue 3, 1999, Pages 659-679

Two interior-point methods for nonlinear P*(τ)-complementarity problems

Author keywords

Interior point algorithms; Nonlinear P* complementarity problems; Polynomial complexity; Scaled Lipschitz condition

Indexed keywords

COMPLEMENTARITY PROBLEMS; GLOBAL CONVER-GENCE; INTERIOR POINT ALGORITHM; INTERIOR-POINT METHOD; LIPSCHITZ; LIPSCHITZ CONDITIONS; NONLINEAR P*-COMPLEMENTARITY PROBLEM; POLYNOMIAL COMPLEXITY; SCALED LIPSCHITZ CONDITION; WIDE NEIGHBORHOOD OF THE CENTRAL PATH;

EID: 0033196647     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022606324827     Document Type: Article
Times cited : (14)

References (32)
  • 1
    • 0032351325 scopus 로고    scopus 로고
    • Global and local quadratic convergence of a long-step adaptive-mode interior-point methods for some monotone variational inequality problems
    • 1. SUN, J., and ZHAO, G., Global and Local Quadratic Convergence of a Long-Step Adaptive-Mode Interior-Point Methods for Some Monotone Variational Inequality Problems, SIAM Journal on Optimization, Vol. 8, pp. 123-139, 1998.
    • (1998) SIAM Journal on Optimization , vol.8 , pp. 123-139
    • Sun, J.1    Zhao, G.2
  • 3
    • 0000772810 scopus 로고
    • Complementarity problems
    • Springer Verlag, Berlin, Germany
    • 3. ISAC, G., Complementarity Problems, Lecture Notes in Mathematics, Springer Verlag, Berlin, Germany, Vol. 1528, 1992.
    • (1992) Lecture Notes in Mathematics , vol.1528
    • Isac, G.1
  • 4
    • 0344704362 scopus 로고
    • Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms, and applications
    • 4. HARKER, P. T., and PANG, J. S., Finite-Dimensional Variational Inequality and Nonlinear Complementarity Problems: A Survey of Theory, Algorithms, and Applications, Mathematical Programming, Vol. 48, pp. 161-220, 1990.
    • (1990) Mathematical Programming , vol.48 , pp. 161-220
    • Harker, P.T.1    Pang, J.S.2
  • 5
    • 84972492753 scopus 로고
    • The analogue of Moreau's proximation theorem, with application to the nonlinear complementarity problem
    • 5. MCLINDEN, L., The Analogue of Moreau's Proximation Theorem, with Application to the Nonlinear Complementarity Problem, Pacific Journal of Mathematics, Vol. 88, pp. 101-161, 1980.
    • (1980) Pacific Journal of Mathematics , vol.88 , pp. 101-161
    • McLinden, L.1
  • 8
    • 0031537871 scopus 로고    scopus 로고
    • A family of polynomial affine scaling algorithms for positive-semidefinite linear complementarity problems
    • 8. JANSEN, B., ROOS, C., and TERLAKY, T., A Family of Polynomial Affine Scaling Algorithms for Positive-Semidefinite Linear Complementarity Problems, SIAM Journal on Optimization, Vol. 7, pp. 126-140, 1997.
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 126-140
    • Jansen, B.1    Roos, C.2    Terlaky, T.3
  • 9
    • 0009139498 scopus 로고    scopus 로고
    • Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems
    • 9. JANSEN, B., ROOS, C., TERLAKY, T., and YOSHISE, A., Polynomiality of Primal-Dual Affine Scaling Algorithms for Nonlinear Complementarity Problems, Mathematical Programming, Vol. 78, pp. 315-345, 1997.
    • (1997) Mathematical Programming , vol.78 , pp. 315-345
    • Jansen, B.1    Roos, C.2    Terlaky, T.3    Yoshise, A.4
  • 10
    • 0003212154 scopus 로고
    • A unified approach to interior-point algorithms for linear complementarity problems
    • Springer Verlag, Berlin, Germany
    • 10. KOJIMA, M., MEGIDDO, N., NOMA, T., and YOSHISE, A., A Unified Approach to Interior-Point Algorithms for Linear Complementarity Problems, Lecture Notes in Computer Sciences, Springer Verlag, Berlin, Germany, Vol. 538, 1991.
    • (1991) Lecture Notes in Computer Sciences , vol.538
    • Kojima, M.1    Megiddo, N.2    Noma, T.3    Yoshise, A.4
  • 11
    • 0009290011 scopus 로고
    • An interior-point potential reduction algorithm for the linear complementarity problem
    • 11. KOJIMA, M., MEGIDDO, N., and YE, Y., An Interior-Point Potential Reduction Algorithm for the Linear Complementarity Problem, Mathematical Programming, Vol. 54, pp. 276-279, 1992.
    • (1992) Mathematical Programming , vol.54 , pp. 276-279
    • Kojima, M.1    Megiddo, N.2    Ye, Y.3
  • 12
    • 0024303530 scopus 로고
    • A new continuation method for complementarity problems with uniform P-functions
    • 12. KOJIMA, M., MIZUNO, S., and NOMA, T., A New Continuation Method for Complementarity Problems with Uniform P-functions, Mathematical Programming, Vol. 43, pp. 107-113, 1989.
    • (1989) Mathematical Programming , vol.43 , pp. 107-113
    • Kojima, M.1    Mizuno, S.2    Noma, T.3
  • 13
    • 0024665751 scopus 로고
    • A polynomial-time algorithm for a class of linear complementarity problems
    • 13. KOJIMA, M., MIZUNO, S., and YOSHISE, A., A Polynomial-Time Algorithm for a Class of Linear Complementarity Problems, Mathematical Programming, Vol. 44, pp. 1-26, 1989.
    • (1989) Mathematical Programming , vol.44 , pp. 1-26
    • Kojima, M.1    Mizuno, S.2    Yoshise, A.3
  • 14
    • 0026171528 scopus 로고
    • 1/2L) iteration potential reduction algorithm for linear complementarity problems
    • 1/2L) Iteration Potential Reduction Algorithm for Linear Complementarity Problems, Mathematical Programming, Vol. 50, pp. 331-342, 1991.
    • (1991) Mathematical Programming , vol.50 , pp. 331-342
    • Kojima, M.1    Mizuno, S.2    Yoshise, A.3
  • 15
    • 58149365648 scopus 로고
    • *-matrix linear complementarity problems
    • *-Matrix Linear Complementarity Problems, Mathematical Programming, Vol. 69, pp. 355-368, 1995.
    • (1995) Mathematical Programming , vol.69 , pp. 355-368
    • Miao, J.M.1
  • 16
    • 0000836925 scopus 로고
    • On the adaptive-step primal-dual interior-point algorithms for linear programming
    • 16. MIZUNO, M., TODD, M. J., and YE, Y., On the Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming, Mathematics of Operations Research, Vol. 18, pp. 964-981, 1993.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 964-981
    • Mizuno, M.1    Todd, M.J.2    Ye, Y.3
  • 17
    • 0030537448 scopus 로고    scopus 로고
    • Interior-point methods for monotone complementarity problems
    • 17. POTRA, F. A., and YE, Y., Interior-Point Methods for Monotone Complementarity Problems, Journal of Optimization Theory and Applications, Vol. 88, pp. 617-642, 1996.
    • (1996) Journal of Optimization Theory and Applications , vol.88 , pp. 617-642
    • Potra, F.A.1    Ye, Y.2
  • 18
    • 0031094383 scopus 로고    scopus 로고
    • A predictor-corrector algorithm for a class of nonlinear saddle-point problems
    • 18. SUN, J., ZHU, J.. and ZHAO, G., A Predictor-Corrector Algorithm for a Class of Nonlinear Saddle-Point Problems, SIAM Journal on Control and Optimization, Vol. 35, pp. 532-551, 1997.
    • (1997) SIAM Journal on Control and Optimization , vol.35 , pp. 532-551
    • Sun, J.1    Zhu, J.2    Zhao, G.3
  • 19
    • 0031533899 scopus 로고    scopus 로고
    • An infeasible path-following method for monotone complementarity problems
    • 19. TSENG, P., An Infeasible Path-Following Method for Monotone Complementarity Problems, SIAM Journal on Optimization, Vol. 7, pp. 386-402, 1997.
    • (1997) SIAM Journal on Optimization , vol.7 , pp. 386-402
    • Tseng, P.1
  • 20
    • 0003205456 scopus 로고
    • A further result on the potential reduction algorithm for the P-matrix linear complementarity problems
    • Edited by P. Pardalos, North-Holland, New York, New York
    • 20. YE, Y., A Further Result on the Potential Reduction Algorithm for the P-Matrix Linear Complementarity Problems, Advances in Optimization and Parallel Computing, Edited by P. Pardalos, North-Holland, New York, New York, pp. 310-316, 1992.
    • (1992) Advances in Optimization and Parallel Computing , pp. 310-316
    • Ye, Y.1
  • 21
    • 0007469893 scopus 로고
    • A class of linear complementarity problems solvable in polynomial time
    • 21. YE, Y., and PARDALOS, P. M., A Class of Linear Complementarity Problems Solvable in Polynomial Time, Linear Algebra and Its Applications, Vol. 152, pp. 2-17, 1991.
    • (1991) Linear Algebra and Its Applications , vol.152 , pp. 2-17
    • Ye, Y.1    Pardalos, P.M.2
  • 22
    • 0027803251 scopus 로고
    • 1/2L) convergence of predictor-corrector algorithms for LCP
    • 1/2L) Convergence of Predictor-Corrector Algorithms for LCP, Mathematical Programming, Vol. 62, pp. 537-551, 1993.
    • (1993) Mathematical Programming , vol.62 , pp. 537-551
    • Ye, Y.1    Anstreicher, K.M.2
  • 23
    • 0001402013 scopus 로고    scopus 로고
    • *(τ)-matrix LCP from arbitrary positive starting points
    • *(τ)-Matrix LCP from Arbitrary Positive Starting Points, Mathematical Programming, Vol. 76, pp. 223-244, 1996.
    • (1996) Mathematical Programming , vol.76 , pp. 223-244
    • Potra, F.A.1    Sheng, R.2
  • 25
    • 0009208154 scopus 로고
    • A superlinearly convergent infeasible-interior-point algorithm for degenerate LCP
    • Department of Mathematics, University of Iowa, Iowa City, Iowa
    • 25. POTRA, F. A., and SHENG, R., A Superlinearly Convergent Infeasible-Interior-Point Algorithm for Degenerate LCP, Computational Mathematics Report, Department of Mathematics, University of Iowa, Iowa City, Iowa, 1994.
    • (1994) Computational Mathematics Report
    • Potra, F.A.1    Sheng, R.2
  • 27
    • 0026954635 scopus 로고
    • Global linear convergence of a path-following algorithm for some monotone variational inequality problems
    • 27. TSENG, P., Global Linear Convergence of a Path-Following Algorithm for Some Monotone Variational Inequality Problems, Journal of Optimization Theory and Applications, Vol. 75, pp. 265-279, 1992.
    • (1992) Journal of Optimization Theory and Applications , vol.75 , pp. 265-279
    • Tseng, P.1
  • 28
    • 0000444718 scopus 로고
    • A path-following algorithm for a class of convex programming problems
    • 28. ZHU, J., A Path-Following Algorithm for a Class of Convex Programming Problems, Zeitschrift für Operations Research, Vol. 36, pp. 359-377, 1992.
    • (1992) Zeitschrift für Operations Research , vol.36 , pp. 359-377
    • Zhu, J.1
  • 29
    • 0031487170 scopus 로고    scopus 로고
    • A modified primal-path-following scheme for the monotone variational inequality problem
    • 29. WU, J. H., A Modified Primal-Path-Following Scheme for the Monotone Variational Inequality Problem, Journal of Optimization Theory and Applications, Vol. 95, pp. 189-208, 1997.
    • (1997) Journal of Optimization Theory and Applications , vol.95 , pp. 189-208
    • Wu, J.H.1
  • 31
    • 0039268804 scopus 로고    scopus 로고
    • Determining the handicap of a sufficient matrix
    • 31. VÄLIAHO, H., Determining the Handicap of a Sufficient Matrix, Linear Algebra and Its Applications, Vol. 253, pp. 279-298, 1997.
    • (1997) Linear Algebra and Its Applications , vol.253 , pp. 279-298
    • Väliaho, H.1
  • 32
    • 0000056529 scopus 로고    scopus 로고
    • Exceptional family for a variational inequality and its applications
    • 32. ZHAO, Y. B., and HAN, J. Y., Exceptional Family for a Variational Inequality and Its Applications, Journal of Global Optimization, Vol. 14, 1999.
    • (1999) Journal of Global Optimization , vol.14
    • Zhao, Y.B.1    Han, J.Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.