论文信息 - A unification of the existence theorems of the nonlinear complementarity problem

A unification of the existence theorems of the nonlinear complementarity problem

The nonlinear complementarity problem is the problem of finding a point x in the n-dimensional Euclidean space,Rn, such that x ⩾ 0, f(x) ⩾ 0 and 〈x,f(x)∼ = 0, where f is a nonlinear continuous function fromRn into itself. Many existence theorems for the problem have been established in various ways. The aim of the present paper is to treat them in a unified manner. Eaves's basic theorem of complementarity is generalized, and the generalized theorem is used as a unified framework for several typical existence theorems.

Masakazu Kojima | M. Kojima

[1] Jorge J. Moré,et al. Classes of functions and feasibility conditions in nonlinear complementarity problems , 1974, Math. Program..

[2] J. J. Moré. Coercivity Conditions in Nonlinear Complementarity Problems , 1974 .

[3] Louis J. Billera,et al. Some recent results inn-person game theory , 1971, Math. Program..

[4] C. E. Lemke,et al. Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[5] Richaard W. Cottle. Nonlinear Programs with Positively Bounded Jacobians , 1966 .

[6] 小島政和. Computational methods for solving the nonlinear complementarity problem , 1974 .

[7] B. Curtis Eaves,et al. Polymatrix Games with Joint Constraints , 1973 .

[8] L. Billera. Some theorems on the core of an n-Game without Side-Payments , 1970 .

[9] B. Curtis Eaves,et al. On the basic theorem of complementarity , 1971, Math. Program..

[10] S. Karamardian,et al. The complementarity problem , 1972, Math. Program..

[11] H. Scarf. The Core of an N Person Game , 1967 .

[12] John Freidenfelds. Fixed-point algorithms and almost-complementary sets , 1971 .

[13] Arie Tamir,et al. Minimality and complementarity properties associated with Z-functions and M-functions , 1974, Math. Program..

[14] G. Dantzig,et al. COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .