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1996-1997 | 24 | 2 | 113-125
Tytuł artykułu

The implicit generalized order complementarity problem and Leontief's input-output model

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the Implicit Generalized Order Complementarity Problem and we use this mathematical model to study a nonlinear and conceptual generalization of Leontief's input-output economic model. We suppose that the economic system works with several technologies and the considered functions are not necessarily increasing.
Rocznik
Tom
24
Numer
2
Strony
113-125
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-02-10
poprawiono
1996-02-09
Twórcy
autor
  • Department of Mathematics, Royal Military College of Canada, Kingston, Ontario, Canada, K7K 5L0
autor
  • Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-1907, U.S.A.
Bibliografia
  • [1] Y. M. Bershchanskiĭ and M. V. Meerov, The complementarity problem: theory and methods of solution, Automat. Remote Control 44 Part I (1983), 687-710.
  • [2] P. Bod, On closed sets having a least element, in: Lecture Notes in Econom. and Math. Systems 177, Springer, 1976, 23-34.
  • [3] P. Bod, Sur un modèle non-linéaire de rapports interindustriels, RAIRO Rech. Opér. 11 (1977), 405-415.
  • [4] J. M. Borwein and M. A. H. Dempster, The linear order complementarity problem, Math. Oper. Res. 14 (1989), 534-558.
  • [5] R. W. Cottle, J. S. Pang and R. E. Stone, The Linear Complementarity Problem, Academic Press, 1992.
  • [6] A. Ebiefung and M. Kostreva, The generalized Leontief input-output model and its application to the choice of new technology, Ann. Oper. Res. 44 (1993), 161-172.
  • [7] E. A. Galperin, The cubic algorithm, J. Math. Anal. Appl. 112 (1985), 635-640.
  • [8] C. R. Glassey, A quadratic network optimization model for equilibrium simple commodity trade flow, Mat. Programming 14 (1978), 98-107.
  • [9] K. Glashoff and B. Werner, Inverse monotonicity of monotone L-operator with applications to quasilinear and free boundary value problems, J. Math. Anal. Appl. 72 (1979), 89-105.
  • [10] D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11 (1987), 623-632.
  • [11] G. Isac, Problèmes de complementarité (en dimension infinie), Publ. Dépt. Math. Univ. Limoges, 1985.
  • [12] G. Isac, Complementarity problem and coincidence equations on convex cones, Boll. Un. Mat. Ital. B 6 (1986), 925-943.
  • [13] G. Isac, Complementarity Problems, Lecture Notes in Math. 1528, Springer, 1992.
  • [14] G. Isac, Iterative methods for the general order complementarity problem, in: Approximation Theory, Spline Functions and Applications, S. P. Singh (ed.), Kluwer Acad. Publ., 1992, 365-380.
  • [15] G. Isac and M. Kostreva, The generalized order complementarity problem, J. Optim. Theory Appl. 71 (1991), 517-534.
  • [16] G. Isac and M. Kostreva, Kneser's theorem and the multivalued generalized order complementarity problem, Appl. Math. Lett. 4 (6) (1991), 81-85.
  • [17] L. G. Khanin, Kantorovich-Rubinshtein duality for Lipschitz spaces defined by differences of arbitrary order, Soviet Math. Dokl. 42 (1991), 220-224.
  • [18] A. Kufner, O. John and S. Fučík, Function Spaces, Noordhoff, 1977.
  • [19] J. Łoś and M. W. Łoś (eds.), Mathematical Models in Economics, PWN and North-Holland, 1974.
  • [20] J. Łoś and M. W. Łoś (eds.), Computing Equilibria: How and Why?, PWN and North-Holland, 1978.
  • [21] L. Mathiesen, Computational experience in solving equilibrium models by a sequence of linear complementarity problems, Oper. Res. 33 (1985), 1225-1250.
  • [22] V. I. Opoĭtsev, A generalization of the theory of monotone and concave operators, Trans. Moscow Math. Soc. 2 (1979), 243-279.
  • [23] J. S. Pang, I. Kaneko and W. P. Hallman, On the solution of some (parametric) linear complementarity problems with applications to portfolio selection, structural engineering and actuarial graduation, Math. Programming 16 (1979), 325-347.
  • [24] J. S. Pang and P. S. C. Lee, A parametric linear complementarity technique for the computation of equilibrium prices in a single commodity spatial model, ibid. 20 (1981), 81-102.
  • [25] O. Paris, Revenue and cost uncertainty generalized mean-variance and the linear complementarity problem, Amer. J. Agricultural Econom. 61 (1979), 268-275.
  • [26] A. L. Peressini, Ordered Topological Vector Spaces, Harper & Row, 1967.
  • [27] E. L. Peterson, The conical duality and complementarity of price and quality for multicommodity spatial and temporal network allocation problem, Discussion paper 207, Center for Mathematical Studies in Economics and Management Science, Northwestern Univ., 1976.
  • [28] M. H. Schneider, Single-commodity spatial equilibria: a network complementarity approach, Ph.D. Thesis, Dept. Industrial Engineering and Management Sciences, Northwestern Univ., Evanston, Ill., 1984.
  • [29] F. Schulz, Regularity Theory for Quasilinear Elliptic Systems and Monge-Ampère Equations in Two Dimensions, Lecture Notes in Math. 1445, Springer, Berlin, 1990.
  • [30] A. Tamir, Minimality and complementarity properties associated with Z-functions and M-functions, Math. Programming 7 (1974), 17-31.
  • [31] J. von Neumann, A model of general economic equilibrium, Rev. Econom. Stud. 13 (1945/1946), 1-9.
  • [32] R. Wilson, Bilinear complementarity problem and competitive equilibria of piecewise linear economic model, Econometrica 46 (1978), 87-103.
  • [33] G. Wintgen, Indifferente Optimierungs Problem, Beitrag zur Internationalen Tagung, Mathematik und Kybernetik in der Ökonomie, Berlin, 1964, Konfe- renzprotokoll, Teil II, Akademie-Verlag, Berlin, 3-6.
  • [34] J. C. Yao, A basic theorem of complementarity for the generalized variational-like inequality problem, J. Math. Anal. Appl. 158 (1991), 124-138; The generalized quasi-variational inequality problem with applications, ibid., 139-160.
  • [35] Q. Zheng, Optimality conditions for global optimization (I) and (II), Acta Math. Appl. Sinica 1 (2, 3) (1985), 66-78 and 118-132.
  • [36] Q. Zheng, Robust analysis and global optimization, Internat. J. Computers Math. Appl. 21 (6/7) (1991), 17-24.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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