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Volumn 583, Issue , 2007, Pages 3-31

Combined relaxation methods for generalized monotone variational inequalities

Author keywords

Classes of applications; Combined relaxation methods; Convergence; Generalized monotone mappings; Variational inequalities

Indexed keywords


EID: 53849106100     PISSN: 00758442     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-37007-9_1     Document Type: Conference Paper
Times cited : (25)

References (49)
  • 1
    • 0000026159 scopus 로고
    • The relaxation method for linear inequalities
    • Agmon S (1954): The relaxation method for linear inequalities. Canadian Journal of Mathematics 6: 382-392
    • (1954) Canadian Journal of Mathematics , vol.6 , pp. 382-392
    • Agmon, S.1
  • 3
    • 20744441937 scopus 로고
    • Competitive stability under weak gross substitutability: The "Euclidean distance" approach
    • Arrow KJ, Hurwicz L (1960): Competitive stability under weak gross substitutability: The "Euclidean distance" approach, International Economic Review 1: 38-49
    • (1960) International Economic Review , vol.1 , pp. 38-49
    • Arrow, K.J.1    Hurwicz, L.2
  • 5
    • 0004068751 scopus 로고
    • Belen'kii VZ, Volkonskii VA (eds, Nauka, Moscow in Russian
    • Belen'kii VZ, Volkonskii VA (eds) (1974): Iterative methods in game theory and programming. Nauka, Moscow (in Russian)
    • (1974) Iterative methods in game theory and programming
  • 7
    • 0001054069 scopus 로고
    • Calcolo approsimato per le soluzioni dei sistemi de equazioni Iineari.
    • Cimmino G (1938): Calcolo approsimato per le soluzioni dei sistemi de equazioni Iineari. La Ricerca Scientifica XVI 1, 326-333
    • (1938) La Ricerca Scientifica , vol.XVI 1 , pp. 326-333
    • Cimmino, G.1
  • 8
    • 0038177483 scopus 로고
    • The relaxation method of solving systems of inequalities with convex functions on the left-hand sides
    • Eremin II (1965): The relaxation method of solving systems of inequalities with convex functions on the left-hand sides. Soviet Mathematics Doklady 6: 219-222
    • (1965) Soviet Mathematics Doklady , vol.6 , pp. 219-222
    • Eremin, I.I.1
  • 11
    • 33646436292 scopus 로고    scopus 로고
    • Handbook of generalized convexity and generalized monotonicity.
    • Hadjisavvas N, Komlósi S, Schaible S eds, Springer, New York
    • Hadjisavvas N, Komlósi S, Schaible S (eds) (2005): Handbook of generalized convexity and generalized monotonicity. "Nonconvex optimization and applications", Vol.76. Springer, New York
    • (2005) Nonconvex optimization and applications , vol.76
  • 13
    • 0016941970 scopus 로고
    • Complementarity over cones with monotone and pseudomonotone maps
    • Karamardian S (1976): Complementarity over cones with monotone and pseudomonotone maps. Journal of Optimization Theory and Applications 18: 445-454
    • (1976) Journal of Optimization Theory and Applications , vol.18 , pp. 445-454
    • Karamardian, S.1
  • 14
    • 0003223272 scopus 로고    scopus 로고
    • On the Stampacchia and Minty variational inequalities
    • Giorgi G, Rossi F eds, Pitagora Editrice, Bologna
    • Komlósi S (1999): On the Stampacchia and Minty variational inequalities. In: Giorgi G, Rossi F (eds) Generalized convexity and optimization in economic and financial decisions. Pitagora Editrice, Bologna, 231-260
    • (1999) Generalized convexity and optimization in economic and financial decisions , pp. 231-260
    • Komlósi, S.1
  • 15
    • 53849085947 scopus 로고
    • A subgradient method of successive relaxation for solving optimization problems. Preprint VINITI No. 531-83, Kazan University, Kazan
    • in Russian
    • Konnov IV (1982): A subgradient method of successive relaxation for solving optimization problems. Preprint VINITI No. 531-83, Kazan University, Kazan (in Russian)
    • (1982)
    • Konnov, I.V.1
  • 16
    • 53849122104 scopus 로고    scopus 로고
    • Konnov IV (1984): A method of the conjugate subgradient type for minimization of functional. Issledovaniya po Prikladnoi Matematike 12: 59-62 (Engl, transl. in Journal of Soviet Mathematics 45: 1026-1029, 1989).
    • Konnov IV (1984): A method of the conjugate subgradient type for minimization of functional. Issledovaniya po Prikladnoi Matematike 12: 59-62 (Engl, transl. in Journal of Soviet Mathematics 45: 1026-1029, 1989).
  • 17
    • 53849126976 scopus 로고    scopus 로고
    • Konnov IV (1993): Combined relaxation methods for finding equilibrium points and solving related problems, Russian Mathematics (Iz. VUZ) 37 (2): 44-51
    • Konnov IV (1993): Combined relaxation methods for finding equilibrium points and solving related problems, Russian Mathematics (Iz. VUZ) 37 (2): 44-51
  • 18
    • 53849117260 scopus 로고    scopus 로고
    • Konnov IV (1993): On combined relaxation method's convergence rates. Russian Mathematics (Iz. VUZ) 37(12): 89-92
    • Konnov IV (1993): On combined relaxation method's convergence rates. Russian Mathematics (Iz. VUZ) 37(12): 89-92
  • 19
    • 53849121069 scopus 로고    scopus 로고
    • Konnov IV (1994): Applications of the combined relaxation method to finding equilibrium points of a quasi-convex-concave function. Russian Mathematics (Iz. VUZ) 38 (12): 66-71
    • Konnov IV (1994): Applications of the combined relaxation method to finding equilibrium points of a quasi-convex-concave function. Russian Mathematics (Iz. VUZ) 38 (12): 66-71
  • 20
    • 0002504482 scopus 로고    scopus 로고
    • A general approach to finding stationary points and the solution of related problems
    • Konnov IV (1996): A general approach to finding stationary points and the solution of related problems. Computational Mathematics and Mathematical Physics 36: 585-593
    • (1996) Computational Mathematics and Mathematical Physics , vol.36 , pp. 585-593
    • Konnov, I.V.1
  • 21
    • 0031515563 scopus 로고    scopus 로고
    • A class of combined iterative methods for solving variational inequalities
    • Konnov IV (1997): A class of combined iterative methods for solving variational inequalities. Journal of Optimization Theory and Applications 94, 677-693
    • (1997) Journal of Optimization Theory and Applications , vol.94 , pp. 677-693
    • Konnov, I.V.1
  • 23
    • 0000134798 scopus 로고    scopus 로고
    • A combined relaxation method for variational inequalities with nonlinear constraints
    • Konnov IV (1998): A combined relaxation method for variational inequalities with nonlinear constraints. Mathematical Programming 80: 239-252
    • (1998) Mathematical Programming , vol.80 , pp. 239-252
    • Konnov, I.V.1
  • 24
    • 0031676560 scopus 로고    scopus 로고
    • On the convergence of combined relaxation methods for variational inequalities
    • Konnov IV (1998): On the convergence of combined relaxation methods for variational inequalities. Optimization Methods and Software 9: 77-92
    • (1998) Optimization Methods and Software , vol.9 , pp. 77-92
    • Konnov, I.V.1
  • 25
    • 53849100133 scopus 로고    scopus 로고
    • Konnov IV (1998): An inexact combined relaxation method for multivalued inclusions. Russian Mathematics (Iz. VUZ) 42 (12): 55-59
    • Konnov IV (1998): An inexact combined relaxation method for multivalued inclusions. Russian Mathematics (Iz. VUZ) 42 (12): 55-59
  • 26
    • 23044479578 scopus 로고    scopus 로고
    • A combined method for variational inequalities with monotone operators
    • Konnov IV (1999): A combined method for variational inequalities with monotone operators. Computational Mathematics and Mathematical Physics 39:1051-1056
    • (1999) Computational Mathematics and Mathematical Physics , vol.39 , pp. 1051-1056
    • Konnov, I.V.1
  • 27
    • 0006031030 scopus 로고    scopus 로고
    • Combined relaxation methods for variational inequality problems over product sets
    • Konnov IV (1999): Combined relaxation methods for variational inequality problems over product sets. Lobachevskii Journal of Mathematics 2: 3-9
    • (1999) Lobachevskii Journal of Mathematics , vol.2 , pp. 3-9
    • Konnov, I.V.1
  • 28
    • 0032671793 scopus 로고    scopus 로고
    • Combined relaxation method for decomposable variational inequalities
    • Konnov IV (1999): Combined relaxation method for decomposable variational inequalities. Optimization Methods and Software 10: 711-728
    • (1999) Optimization Methods and Software , vol.10 , pp. 711-728
    • Konnov, I.V.1
  • 30
    • 53849113466 scopus 로고    scopus 로고
    • Konnov IV (2001): Combined relaxation method for extended variational inequalities. Russian Mathematics (Iz. VUZ) 45 (12): 46-54
    • Konnov IV (2001): Combined relaxation method for extended variational inequalities. Russian Mathematics (Iz. VUZ) 45 (12): 46-54
  • 31
    • 0036526064 scopus 로고    scopus 로고
    • A combined relaxation method for nonlinear variational inequalities
    • Konnov IV (2002): A combined relaxation method for nonlinear variational inequalities. Optimization Methods and Software 17: 271-292
    • (2002) Optimization Methods and Software , vol.17 , pp. 271-292
    • Konnov, I.V.1
  • 32
    • 0036486921 scopus 로고    scopus 로고
    • A class of combined relaxation methods for decomposable variational inequalities
    • Konnov IV (2002): A class of combined relaxation methods for decomposable variational inequalities. Optimization 51: 109-125
    • (2002) Optimization , vol.51 , pp. 109-125
    • Konnov, I.V.1
  • 33
    • 0036486926 scopus 로고    scopus 로고
    • A combined relaxation method for a class of nonlinear variational inequalities
    • Konnov IV (2002): A combined relaxation method for a class of nonlinear variational inequalities. Optimization 51: 127-143
    • (2002) Optimization , vol.51 , pp. 127-143
    • Konnov, I.V.1
  • 34
    • 0042884758 scopus 로고
    • On the generalization of a direct method of the calculus of variations
    • Minty G (1967): On the generalization of a direct method of the calculus of variations. Bulletin of the American Mathematical Society 73: 315-321
    • (1967) Bulletin of the American Mathematical Society , vol.73 , pp. 315-321
    • Minty, G.1
  • 41
    • 0018922522 scopus 로고
    • Existence and uniqueness of equilibrium points for concave ?i-person games
    • Rosen JB (1965): Existence and uniqueness of equilibrium points for concave ?i-person games. Econometrica, 33: 520-534
    • (1965) Econometrica , vol.33 , pp. 520-534
    • Rosen, J.B.1
  • 42
    • 0000120951 scopus 로고
    • The non-transitive consumer
    • Shafer W (1974): The non-transitive consumer. Econometrica 42: 913-919
    • (1974) Econometrica , vol.42 , pp. 913-919
    • Shafer, W.1
  • 43
    • 38249028742 scopus 로고
    • Browder-Hartmann-Stampacchia, variational inequalities for multivalued monotone operators
    • Shih MH, Tan KK (1988): Browder-Hartmann-Stampacchia, variational inequalities for multivalued monotone operators. Journal of Mathematical Analysis and Applications 134: 431-440
    • (1988) Journal of Mathematical Analysis and Applications , vol.134 , pp. 431-440
    • Shih, M.H.1    Tan, K.K.2
  • 45
  • 46
    • 58149412614 scopus 로고
    • Intransitivity of preferences
    • Tversky A (1969): Intransitivity of preferences. Psychological Review 76: 31-48
    • (1969) Psychological Review , vol.76 , pp. 31-48
    • Tversky, A.1
  • 48
    • 0037335897 scopus 로고    scopus 로고
    • Some recent advances in projection-type methods for variational inequalities
    • Xiu N, Zhang J (2003): Some recent advances in projection-type methods for variational inequalities. Journal of Computational and Applied Mathematics 152: 559-585
    • (2003) Journal of Computational and Applied Mathematics , vol.152 , pp. 559-585
    • Xiu, N.1    Zhang, J.2
  • 49
    • 0028545469 scopus 로고
    • Multivalued variational inequalities with K - pseudomonotone operators
    • Yao JC (1994): Multivalued variational inequalities with K - pseudomonotone operators. Journal of Optimization Theory and Applications 83: 391-403
    • (1994) Journal of Optimization Theory and Applications , vol.83 , pp. 391-403
    • Yao, J.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.