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Volumn 116, Issue 1-4, 2002, Pages 199-221

Solvability of implicit complementarity problems

Author keywords

Continuous selections; Exceptional families; Existence alternatives; Implicit complementarity problem

Indexed keywords


EID: 0036452820     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/A:1021388515849     Document Type: Conference Paper
Times cited : (16)

References (56)
  • 4
    • 22044448726 scopus 로고    scopus 로고
    • A Leray-Schauder type theorem for approximable maps: A simple proof
    • H. Ben-el-Mechaiekh, S. Chebbi and M. Florenzano, A Leray-Schauder type theorem for approximable maps: A simple proof, Proc. Amer. Math. Soc. 126 (1998) 2345-2349.
    • (1998) Proc. Amer. Math. Soc. , vol.126 , pp. 2345-2349
    • Ben-el-Mechaiekh, H.1    Chebbi, S.2    Florenzano, M.3
  • 5
    • 84966239133 scopus 로고
    • A Leray-Schauder type theorem for approximable maps
    • H. Ben-el-Mechaiekh and A. Idzik, A Leray-Schauder type theorem for approximable maps, Proc. Amer. Math. Soc. 122 (1994) 105-109.
    • (1994) Proc. Amer. Math. Soc. , vol.122 , pp. 105-109
    • Ben-el-Mechaiekh, H.1    Idzik, A.2
  • 6
    • 0001109147 scopus 로고
    • Contrôle impulsionnel et inéquations quasivariationnelles stationaires
    • A. Bensoussan, M. Gourset and J.-L. Lions, Contrôle impulsionnel et inéquations quasivariationnelles stationaires, C. R. Acad. Sci. Paris, Ser. A-B 276 (1973) 1279-1284.
    • (1973) C. R. Acad. Sci. Paris, Ser. A-B , vol.276 , pp. 1279-1284
    • Bensoussan, A.1    Gourset, M.2    Lions, J.-L.3
  • 7
    • 0001441937 scopus 로고
    • Nouvelle formulation de problèmes de contrôle impulsionnel et applications
    • A. Bensoussan and J.-L Lions, Nouvelle formulation de problèmes de contrôle impulsionnel et applications, C. R. Acad. Sci. Paris, Ser. A-B 276 (1973) 1189-1192.
    • (1973) C. R. Acad. Sci. Paris, Ser. A-B , vol.276 , pp. 1189-1192
    • Bensoussan, A.1    Lions, J.-L.2
  • 8
    • 0002442477 scopus 로고    scopus 로고
    • Application of topological degree theory to complementarity problems
    • eds. A. Migdalas, P.M. Pardalos and P. Värbrand (Kluwer, Dordrecht)
    • V.A. Bulavsky, G. Isac and V.V. Kalashnikov, Application of topological degree theory to complementarity problems, in: Multilevel Optimization: Algorithms and Applications, eds. A. Migdalas, P.M. Pardalos and P. Värbrand (Kluwer, Dordrecht, 1998).
    • (1998) Multilevel Optimization: Algorithms and Applications
    • Bulavsky, V.A.1    Isac, G.2    Kalashnikov, V.V.3
  • 11
    • 0000617544 scopus 로고
    • The generalized quasi-variational problem
    • D. Chan and J.-S. Pang, The generalized quasi-variational problem, Math. Oper. Res. 7 (1982) 211-222.
    • (1982) Math. Oper. Res. , vol.7 , pp. 211-222
    • Chan, D.1    Pang, J.-S.2
  • 14
    • 0344704362 scopus 로고
    • Finite-dimensional variational inequalities and nonlinear complementarity problems: A survey of theory, algorithms and applications
    • P.T. Harker and J.-S. Pang, Finite-dimensional variational inequalities and nonlinear complementarity problems: A survey of theory, algorithms and applications, Math. Programming 48 (1990) 161-220.
    • (1990) Math. Programming , vol.48 , pp. 161-220
    • Harker, P.T.1    Pang, J.-S.2
  • 16
    • 84971193292 scopus 로고
    • On the implicit complementarity problem in Hilbert spaces
    • G. Isac, On the implicit complementarity problem in Hilbert spaces, Bull. Austral. Math. Soc. 32 (1985) 251-260.
    • (1985) Bull. Austral. Math. Soc. , vol.32 , pp. 251-260
    • Isac, G.1
  • 17
    • 0007193378 scopus 로고
    • Complementarity problem and coincidence equations on convex cones
    • G. Isac, Complementarity problem and coincidence equations on convex cones, Boll. Un. Mat. Ital. B(6) 5 (1986) 925-943.
    • (1986) Boll. Un. Mat. Ital. B , vol.5 , Issue.6 , pp. 925-943
    • Isac, G.1
  • 18
    • 84974510015 scopus 로고
    • Fixed point theory and complementarity problems in Hilbert spaces
    • G. Isac, Fixed point theory and complementarity problems in Hilbert spaces, Bull. Austral. Math. Soc. 36 (1987) 295-310.
    • (1987) Bull. Austral. Math. Soc. , vol.36 , pp. 295-310
    • Isac, G.1
  • 19
    • 0002694841 scopus 로고
    • Fixed point theory, coincidence equations on convex cones and complementarity problem
    • G. Isac, Fixed point theory, coincidence equations on convex cones and complementarity problem, Contemp. Math. 72 (1988) 139-155.
    • (1988) Contemp. Math. , vol.72 , pp. 139-155
    • Isac, G.1
  • 20
    • 0001386329 scopus 로고
    • A special variational inequality and the implicit complementarity problem
    • G. Isac, A special variational inequality and the implicit complementarity problem, J. Fac. Sci. Univ. Tokyo, Sect. IA, Math. 37 (1990) 109-127.
    • (1990) J. Fac. Sci. Univ. Tokyo, Sect. IA, Math. , vol.37 , pp. 109-127
    • Isac, G.1
  • 21
    • 0003572263 scopus 로고
    • Lecture Notes in Mathematics, (Springer, Berlin)
    • G. Isac, Complementarity Problems, Lecture Notes in Mathematics, Vol. 1528 (Springer, Berlin, 1992).
    • (1992) Complementarity Problems , vol.1528
    • Isac, G.1
  • 22
    • 38249002697 scopus 로고
    • Tikhonov regularization and the complementarity problem in Hilbert spaces
    • G. Isac, Tikhonov regularization and the complementarity problem in Hilbert spaces, J. Math. Anal. Appl. 174 (1993) 53-66.
    • (1993) J. Math. Anal. Appl. , vol.174 , pp. 53-66
    • Isac, G.1
  • 24
    • 0002711201 scopus 로고    scopus 로고
    • A generalization of Karamardian's condition in complementarity theory
    • G. Isac, A generalization of Karamardian's condition in complementarity theory, Nonlinear Anal. Forum 4 (1999) 49-63.
    • (1999) Nonlinear Anal. Forum , vol.4 , pp. 49-63
    • Isac, G.1
  • 26
    • 0034348370 scopus 로고    scopus 로고
    • Exceptional family of elements, feasibility and complementarity
    • G. Isac, Exceptional family of elements, feasibility and complementarity, J. Optim. Theory Appl. 104 (2000) 577-588.
    • (2000) J. Optim. Theory Appl. , vol.104 , pp. 577-588
    • Isac, G.1
  • 27
    • 0007156201 scopus 로고    scopus 로고
    • Exceptional family of elements, feasibility, solvability and continuous paths of ε-solutions for nonlinear complementarity problems
    • ed. P.M. Pardalos (Kluwer, Boston)
    • G. Isac, Exceptional family of elements, feasibility, solvability and continuous paths of ε-solutions for nonlinear complementarity problems, in: Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems, ed. P.M. Pardalos (Kluwer, Boston, 2000).
    • (2000) Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems
    • Isac, G.1
  • 29
    • 0001398951 scopus 로고    scopus 로고
    • Exceptional families, topological degree and complementarity problems
    • G. Isac, V.A. Bulavsky and V.V. Kalashnikov, Exceptional families, topological degree and complementarity problems, J. Global Optim. 10 (1997) 207-225.
    • (1997) J. Global Optim. , vol.10 , pp. 207-225
    • Isac, G.1    Bulavsky, V.A.2    Kalashnikov, V.V.3
  • 30
    • 0002573779 scopus 로고    scopus 로고
    • Exceptional families of elements for continuous functions, some applications to complementarity theory
    • G. Isac and A. Carbone, Exceptional families of elements for continuous functions, some applications to complementarity theory, J. Global Optim. 15 (1999) 181-196.
    • (1999) J. Global Optim. , vol.15 , pp. 181-196
    • Isac, G.1    Carbone, A.2
  • 31
    • 0007323651 scopus 로고
    • Existence theorems for the implicit complementarity problems
    • G. Isac and D. Goeleven, Existence theorems for the implicit complementarity problems, Internit. J. Math. Math. Sci. 16 (1993) 67-74.
    • (1993) Internit. J. Math. Math. Sci. , vol.16 , pp. 67-74
    • Isac, G.1    Goeleven, D.2
  • 32
    • 21344482566 scopus 로고
    • The implicit general order complementarity problem: Models and iterative methods
    • G. Isac and D. Goeleven, The implicit general order complementarity problem: Models and iterative methods, Ann. Oper. Res. 44 (1993) 63-92.
    • (1993) Ann. Oper. Res. , vol.44 , pp. 63-92
    • Isac, G.1    Goeleven, D.2
  • 33
    • 0035534035 scopus 로고    scopus 로고
    • Exceptional families of elements, Leray-Schauder alternatives, pseudomonotone operators and complementarity
    • G. Isac and V.V. Kalashnikov, Exceptional families of elements, Leray-Schauder alternatives, pseudomonotone operators and complementarity, J. Optim. Theory Appl. 109 (2001) 69-83.
    • (2001) J. Optim. Theory Appl. , vol.109 , pp. 69-83
    • Isac, G.1    Kalashnikov, V.V.2
  • 34
    • 0032350865 scopus 로고    scopus 로고
    • Functions without exceptional families of elements and complementarity problems
    • G. Isac and W.T. Obuchowska, Functions without exceptional families of elements and complementarity problems, J. Optim. Theory Appl. 99, (1998) 147-163.
    • (1998) J. Optim. Theory Appl. , vol.99 , pp. 147-163
    • Isac, G.1    Obuchowska, W.T.2
  • 36
    • 0034658809 scopus 로고    scopus 로고
    • Exceptional families of elements and the solvability of variational inequalities for unbounded sets in infinite dimensional Hilbert spaces
    • G. Isac and Y.B. Zhao, Exceptional families of elements and the solvability of variational inequalities for unbounded sets in infinite dimensional Hilbert spaces, J. Math. Anal. Appl. 246 (2000) 544-556.
    • (2000) J. Math. Anal. Appl. , vol.246 , pp. 544-556
    • Isac, G.1    Zhao, Y.B.2
  • 39
    • 0000522174 scopus 로고
    • Generalized complementarity problem
    • S. Karamardian, Generalized complementarity problem, J. Optim. Theory Appl. 8 (1971) 161-168.
    • (1971) J. Optim. Theory Appl. , vol.8 , pp. 161-168
    • Karamardian, S.1
  • 41
    • 0001652704 scopus 로고
    • Selected selection theorems
    • E. Michael, Selected selection theorems, Amer. Math. Monthly 63 (1956) 233-238.
    • (1956) Amer. Math. Monthly , vol.63 , pp. 233-238
    • Michael, E.1
  • 43
    • 0141557706 scopus 로고
    • On some nonlinear quasi-variational inequalities and implicit complementarity problems in stochastic control theory
    • eds. R.W. Cottle, F. Giannessi and J.-L. Lions (Wiley, New York)
    • U. Mosco, On some nonlinear quasi-variational inequalities and implicit complementarity problems in stochastic control theory, in: Variational Inequalities and Complemetarity Problems, Theory and Applications, eds. R.W. Cottle, F. Giannessi and J.-L. Lions (Wiley, New York, 1980).
    • (1980) Variational Inequalities and Complemetarity Problems, Theory and Applications
    • Mosco, U.1
  • 45
    • 0000804782 scopus 로고
    • The implicit complementarity problem
    • eds. O.L. Mangasarian, R.R. Meyer and S.M. Robinson (Academic Press, New York)
    • J.-S. Pang, The implicit complementarity problem, in: Nonlinear Programming IV, eds. O.L. Mangasarian, R.R. Meyer and S.M. Robinson (Academic Press, New York, 1981).
    • (1981) Nonlinear Programming IV
    • Pang, J.-S.1
  • 46
    • 0020143523 scopus 로고
    • On the convergence of a basic iterative method for the implicit complementarity problem
    • J.-S. Pang, On the convergence of a basic iterative method for the implicit complementarity problem, J. Optim. Theory Appl. 37 (1982) 149-162.
    • (1982) J. Optim. Theory Appl. , vol.37 , pp. 149-162
    • Pang, J.-S.1
  • 47
    • 84873015559 scopus 로고    scopus 로고
    • Proc. of Math. Inst. of the Russian Academy of Science (Steklov Institute) (in Russian)
    • D.B. Silin, Some properties of upper semicontinuous multi-valued mappings, Proc. of Math. Inst. of the Russian Academy of Science (Steklov Institute) 185 (1998) 222-235 (in Russian).
    • (1998) Some Properties of Upper Semicontinuous Multi-valued Mappings , vol.185 , pp. 222-235
    • Silin, D.B.1
  • 48
    • 0021519808 scopus 로고
    • A descent algorithm for solving monotone variational inequalities and monotone complementarity problems
    • M.J. Smith, A descent algorithm for solving monotone variational inequalities and monotone complementarity problems, J. Optim. Theory Appl. 44 (1984) 485-496.
    • (1984) J. Optim. Theory Appl. , vol.44 , pp. 485-496
    • Smith, M.J.1
  • 49
    • 0000140189 scopus 로고    scopus 로고
    • Exceptional family and finite-dimensional variational inequality over polyhedral convex set
    • Y.B. Zhao, Exceptional family and finite-dimensional variational inequality over polyhedral convex set, Appl. Math. Comput. 87 (1997) 111-126.
    • (1997) Appl. Math. Comput. , vol.87 , pp. 111-126
    • Zhao, Y.B.1
  • 51
    • 0000056529 scopus 로고    scopus 로고
    • Exceptional family of elements for a variational inequality problem and its applications
    • Y.B. Zhao and J.Y. Han, Exceptional family of elements for a variational inequality problem and its applications, J. Global Optim. 14 (1999) 313-330.
    • (1999) J. Global Optim. , vol.14 , pp. 313-330
    • Zhao, Y.B.1    Han, J.Y.2
  • 52
    • 0033244578 scopus 로고    scopus 로고
    • Exceptional family and existence theorems for variational inequality problems
    • Y.B. Zhao, J.Y. Han and H.D. Qi, Exceptional family and existence theorems for variational inequality problems, J. Optim. Theory Appl. 101 (1999) 475-495.
    • (1999) J. Optim. Theory Appl. , vol.101 , pp. 475-495
    • Zhao, Y.B.1    Han, J.Y.2    Qi, H.D.3
  • 54
    • 0034349271 scopus 로고    scopus 로고
    • Quasi-P* and P(τ, α, β)-maps, exceptional family of elements and complementarity problems
    • Y.B. Zhao and G. Isac, Quasi-P* and P(τ, α, β)-maps, exceptional family of elements and complementarity problems, J. Optim. Theory Appl. 105 (2000) 213-231.
    • (2000) J. Optim. Theory Appl. , vol.105 , pp. 213-231
    • Zhao, Y.B.1    Isac, G.2
  • 55
    • 0034453276 scopus 로고    scopus 로고
    • Properties of a multivalued mapping associated with some non-monotone complementarity problems
    • Y.B. Zhao and G. Isac, Properties of a multivalued mapping associated with some non-monotone complementarity problems, SIAM J. Control Optim. 39 (2000) 571-593.
    • (2000) SIAM J. Control Optim. , vol.39 , pp. 571-593
    • Zhao, Y.B.1    Isac, G.2
  • 56
    • 0035501583 scopus 로고    scopus 로고
    • Alternative theorems for nonlinear projection equations and applications to generalized complementarity problem
    • Y.B. Zhao and D.F. Sun, Alternative theorems for nonlinear projection equations and applications to generalized complementarity problem, Nonlinear Anal. 46 (2001) 853-868.
    • (2001) Nonlinear Anal. , vol.46 , pp. 853-868
    • Zhao, Y.B.1    Sun, D.F.2


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