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The dual approach to one class of mixed variational inequalities. (Russian, English) Zbl 1105.49302

Zh. Vychisl. Mat. Mat. Fiz. 42, No. 9, 1324-1337 (2002); translation in Comput. Math. Math. Phys. 42, No. 9, 1276-1288 (2002).
Summary: The problem of finding a solution to a general class of mixed variational inequalities, which can be interpreted as a generalization of a primal-dual variational inequality, is considered. It is shown that many general problems of economic equilibrium under the conditions of perfect and imperfect competition with allowance for the spatial arrangement of objects are reduced exactly to this class of mixed variational inequalities. The original problem is reduced to the problem of finding a zero of the sum of monotone mappings, and a splitting method is applied to its solution.

MSC:

49J40 Variational inequalities
47J30 Variational methods involving nonlinear operators
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