An algorithm for finding equilibrium in the linear exchange model with fixed budgets

Journal of Applied and Industrial Mathematics - Tập 3 Số 4 - Trang 505-518 - 2009
V. I. Shmyrëv1
1Sobolev Institute of Mathematics

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Tài liệu tham khảo

V. I. Shmyrev, “On an Approach to the Determination of Equilibrium in Pure Exchange Models,” Dokl. Akad. Nauk SSSR 268, 1062–1066 (1983) [Sov. Math., Dokl. 27, 230–233 (1983)].

B. C. Eaves, “A Finite Algorithm for the Linear Exchange Model,” J. Math. Econom. 3(2), 197–204 (1976).

C. E. Lemke, “Bimatrix Equilibrium Points and Mathematical Programming,” Management Sci. 2(7), 681–689 (1965).

V. I. Shmyrev and N. V. Shmyreva, “An Iterative Algorithm for Searching an Equilibrium in the Linear Exchange Model,” Siberian Adv. Math. 6(1), 87–104 (1996).

V. I. Shmyrev, “Algorithms for Determination of an Equilibrium in the Exchange Models with Fixed Budgets,” Optimizatsiya, 31(48) (Inst. Mat., Novosibirsk, 1983), pp. 137–155.

V. I. Shmyrev, “An Algorithmic Approach for Searching an Equilibrium in Fixed Budget Exchange Models,” in Russian Contributions to Game Theory and Equilibrium Theory, Ed. by T. S. H. Driessen, G. van der Laan, V. A. Vasil’ev, and E. B. Yanovskaya (Springer, Berlin, 2006), pp. 217–235.

E. G. Gol’dshtein and D. B. Yudin, Transportation Type Problems (Nauka, Moscow, 1969) [in Russian].

D. Gale, “The Linear Exchange Model,” J. Math. Econom. 3(2), 205–209 (1976).

D. Gale, The Theory of Linear Economic Models (McGraw-Hill, New York, 1960; Inostrannaya Literatura, Moscow, 1963).

V. I. Shmyrev, “An Algorithm for the Search of Equilibrium in a Linear Exchange Model,” Sibirsk. Mat. Zh. 26(2), 163–175 (1985) [Siberian Math. J. 26, 288–300 (1985)].

R. T. Rockafellar, Convex Analysis (Princeton Univ. Press, Princeton, 1970; Mir, Moscow, 1973).

V. I. Shmyrev, Introduction to Mathematical Programming (Inst. Computer Sci., Izhevsk, 2002) [in Russian].

G. Sh. Rubinshtein and V. I. Shmyrev, “Minimization Methods for a Quasiconvex Function on a Convex Polyhedron,” Optimizatsiya, 1(18) (Inst. Mat., Novosibirsk, 1971), pp. 82–117.

G. B. Dantzig and R. W. Cottle, “Positive (Semi-)Definite Programming,” in Nonlinear Programming (Noth-Holland, Amsterdam, 1967), pp. 55–73.