메뉴 건너뛰기




Volumn 370, Issue SUPP, 2003, Pages 355-368

On some interconnections between strict monotonicity, globally uniquely solvable, and P properties in semidefinite linear complementarity problems

Author keywords

Complementarity; Lyapunov; Positive stable; Stein

Indexed keywords

LYAPUNOV METHODS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

EID: 0037623914     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(03)00425-7     Document Type: Article
Times cited : (24)

References (29)
  • 3
    • 0038762712 scopus 로고    scopus 로고
    • Complementarity problems and positive definite matrices
    • Indian Statistical Institute, Street No. 8, Habshiguda, Hyderabad 500 007, India, (Revised June 27, 2001)
    • P. Bhimasankaram, A.L.N. Murthy, G.S.R. Murthy, T. Parthasarathy, Complementarity problems and positive definite matrices, Research Report, Indian Statistical Institute, Street No. 8, Habshiguda, Hyderabad 500 007, India, 2000 (Revised June 27, 2001).
    • (2000) Research Report
    • Bhimasankaram, P.1    Murthy, A.L.N.2    Murthy, G.S.R.3    Parthasarathy, T.4
  • 6
    • 4243203786 scopus 로고    scopus 로고
    • Stability and inertia
    • Datta B.N. Stability and inertia. Linear Algebra Appl. 302-303:1999;563-600.
    • (1999) Linear Algebra Appl. , vol.302-303 , pp. 563-600
    • Datta, B.N.1
  • 7
    • 0004131235 scopus 로고
    • New York: Chelsea Publishing Company
    • Gantmacher F.R. Theory of Matrices, Vol. II. 1959;Chelsea Publishing Company, New York.
    • (1959) Theory of Matrices , vol.2
    • Gantmacher, F.R.1
  • 8
    • 0034356518 scopus 로고    scopus 로고
    • Complementarity forms of the theorems of Lyapunov and Stein, and related results
    • Gowda M.S., Parthasarathy T. Complementarity forms of the theorems of Lyapunov and Stein, and related results. Linear Algebra Appl. 320:2000;131-144.
    • (2000) Linear Algebra Appl. , vol.320 , pp. 131-144
    • Gowda, M.S.1    Parthasarathy, T.2
  • 9
    • 0013349755 scopus 로고    scopus 로고
    • Errata: On semidefinite linear complementarity problems
    • Gowda M.S., Song Y. Errata: On semidefinite linear complementarity problems. Math. Prog. Series A. 88:2000;575-587.
    • (2000) Math. Prog. Series A , vol.88 , pp. 575-587
    • Gowda, M.S.1    Song, Y.2
  • 10
    • 0037748466 scopus 로고    scopus 로고
    • Errata: On semidefinite linear complementarity problems
    • Gowda M.S., Song Y. Errata: On semidefinite linear complementarity problems. Math. Prog. Series A. 91:2001;199-200.
    • (2001) Math. Prog. Series A , vol.91 , pp. 199-200
    • Gowda, M.S.1    Song, Y.2
  • 11
    • 0037281567 scopus 로고    scopus 로고
    • Some new results for the semidefinite linear complementarity problem
    • Gowda M.S., Song Y. Some new results for the semidefinite linear complementarity problem. SIAM J. Matrix Anal. 24:2002;25-39.
    • (2002) SIAM J. Matrix Anal. , vol.24 , pp. 25-39
    • Gowda, M.S.1    Song, Y.2
  • 12
    • 31444442587 scopus 로고    scopus 로고
    • Some interconnections between strict monotonicity, GUS, and P properties in semidefinite linear complementarity problems
    • Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, October
    • M.S. Gowda, Y. Song, G. Ravindran, Some interconnections between strict monotonicity, GUS, and P properties in semidefinite linear complementarity problems, Research Report TR01-11, Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, October 2001.
    • (2001) Research Report , vol.TR01-11
    • Gowda, M.S.1    Song, Y.2    Ravindran, G.3
  • 13
    • 0344704362 scopus 로고
    • Finite dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms, and applications
    • Harker P.T., Pang J.-S. Finite dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms, and applications. Math. Prog. 48:1990;161-220.
    • (1990) Math. Prog. , vol.48 , pp. 161-220
    • Harker, P.T.1    Pang, J.-S.2
  • 15
    • 0031542833 scopus 로고    scopus 로고
    • Interior-point methods for the monotone semidefinite linear complementarity problems
    • Kojima M., Shindoh S., Hara S. Interior-point methods for the monotone semidefinite linear complementarity problems. SIAM Optim. 7:1997;86-125.
    • (1997) SIAM Optim. , vol.7 , pp. 86-125
    • Kojima, M.1    Shindoh, S.2    Hara, S.3
  • 16
    • 0003139490 scopus 로고
    • On ranges of real Lyapunov transformations
    • Loewy R. On ranges of real Lyapunov transformations. Linear Algebra Appl. 13:1976;79-89.
    • (1976) Linear Algebra Appl. , vol.13 , pp. 79-89
    • Loewy, R.1
  • 17
    • 0001525304 scopus 로고
    • Probléme général de la stabilité des mouvement
    • Lyapunov M.A. Probléme général de la stabilité des mouvement, Ann. Fac. Sci. Toulouse 9 (1907) 203-474 (French, translation of the original paper published in 1893 in Comm. Soc. Math. Kharkow; reprinted as vol. 17 in Annals of Mathematics Study, Princeton University Press, Princeton, NJ, 1949
    • (1907) Ann. Fac. Sci. Toulouse , vol.9 , pp. 203-474
    • Lyapunov, M.A.1
  • 18
    • 0013396881 scopus 로고
    • Lyapunov M.A. Probléme général de la stabilité des mouvement, Ann. Fac. Sci. Toulouse 9 (1907) 203-474 (French, translation of the original paper published in 1893 in Comm. Soc. Math. Kharkow; reprinted as vol. 17 in Annals of Mathematics Study, Princeton University Press, Princeton, NJ, 1949
    • (1893) Comm. Soc. Math. Kharkow
  • 19
    • 0007327799 scopus 로고
    • Princeton University Press, Princeton, NJ
    • Lyapunov M.A. Probléme général de la stabilité des mouvement. French, translation of the original paper published in 1893 in Comm. Soc. Math. Kharkow; reprinted as vol. 17 in Annals of Mathematics Study, Princeton University Press, Princeton, NJ, 1949 Ann. Fac. Sci. Toulouse. 9:1907;203-474.
    • (1949) Annals of Mathematics Study , vol.17
  • 20
    • 0031145270 scopus 로고    scopus 로고
    • A cone programming approach to the bilinear matrix inequality problem and its geometry
    • Mesbahi M., Papavassilopoulos G.P. A cone programming approach to the bilinear matrix inequality problem and its geometry. Math. Prog. 77:1997;247-272.
    • (1997) Math. Prog. , vol.77 , pp. 247-272
    • Mesbahi, M.1    Papavassilopoulos, G.P.2
  • 21
    • 0038086967 scopus 로고    scopus 로고
    • Semismooth homeomorphims and strong stability of semidefinite and Lorentz complementarity problems
    • Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland 21228, USA (revised) September
    • J.-S. Pang, D. Sun, J. Sun, Semismooth homeomorphims and strong stability of semidefinite and Lorentz complementarity problems, Research Report, Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, Maryland 21228, USA (revised) September 2002.
    • (2002) Research Report
    • Pang, J.-S.1    Sun, D.2    Sun, J.3
  • 23
    • 0038762710 scopus 로고    scopus 로고
    • 2-property need not imply strong monotonicity in the semidefinite LCPs
    • Indian Statistical Institute, Chennai, June
    • 2-property need not imply strong monotonicity in the semidefinite LCPs, Research Report, Indian Statistical Institute, Chennai, June 2001.
    • (2001) Research Report
    • Parthasarathy, T.1    Sampangi Raman, D.2    Sriparna, B.3
  • 24
    • 0642296091 scopus 로고
    • Positive operators and an inertia theorem
    • Schneider H. Positive operators and an inertia theorem. Numerische Mathematik. 1965;11-17.
    • (1965) Numerische Mathematik , pp. 11-17
    • Schneider, H.1
  • 25
    • 0013393673 scopus 로고
    • Some general theorems on iterants
    • Stein P. Some general theorems on iterants. J. Res. Natl. Bur. Standards. 48:1952;82-83.
    • (1952) J. Res. Natl. Bur. Standards , vol.48 , pp. 82-83
    • Stein, P.1
  • 26
    • 0036474487 scopus 로고    scopus 로고
    • Semismooth matrix valued functions
    • Sun D., Sun J. Semismooth matrix valued functions. Math. Operations Res. 27:2002;150-169.
    • (2002) Math. Operations Res. , vol.27 , pp. 150-169
    • Sun, D.1    Sun, J.2
  • 27
    • 0000882736 scopus 로고    scopus 로고
    • Merit functions for semi-definite complementarity problems
    • Tseng P. Merit functions for semi-definite complementarity problems. Math. Prog. 83:1998;159-185.
    • (1998) Math. Prog. , vol.83 , pp. 159-185
    • Tseng, P.1
  • 29
    • 0037856577 scopus 로고    scopus 로고
    • New York: Springer-Verlag
    • Zhang F. Matrix Theory. 1999;Springer-Verlag, New York.
    • (1999) Matrix Theory
    • Zhang, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.