Invited Session Thu.2.MA 313

Thursday, 13:15 - 14:45 h, Room: MA 313

Cluster 3: Complementarity & variational inequalities [...]

Iterative methods for variational inequalities


Chair: Igor V. Konnov and Vyacheslav V. Kalashnikov



Thursday, 13:15 - 13:40 h, Room: MA 313, Talk 1

Igor V. Konnov
Extended systems of primal-dual variational inequalities


A system of variational inequalities with general mappings,
which can be regarded as an extension of Lagrangean primal-dual systems of constrained problems, is considered.
Many equilibrium type problems can be written in this format.
In particular, we show that this problem is suitable for modelling various complex systems including spatial telecommunication, transportation, and economic ones. However, the basic mappings can be multi-valued and even non-monotone in real applications. This fact creates certain difficulties for providing convergence of many existing iterative methods.
In this talk, we describe several families of iterative solution methods for the above system which are adjusted to the mappings properties. In particular, they are applicable both for the single-valued and for the multi-valued case. Next, the methods are convergent under mild conditions and admit efficient computational implementation especially for
the spatially distributed problems.



Thursday, 13:45 - 14:10 h, Room: MA 313, Talk 2

Alexander Zaslavski
The extragradient method for solving variational inequalities in the presence of computational errors


In a Hilbert space, we study the convergence of
the subgradient method to a solution of a variational inequality,
under the presence of computational errors. Most results known in
the literature establish convergence of optimization algorithms,
when computational errors are summable. In the present paper, the
convergence of the subgradient method for solving variational
inequalities is established for nonsummable computational errors.
We show that the subgradient method generates a good approximate
solution, if the sequence of computational errors is bounded from
above by a constant.



Thursday, 14:15 - 14:40 h, Room: MA 313, Talk 3

Vyacheslav V. Kalashnikov
Finding a conjectural variations equilibrium in a financial model by solving a variational inequality problem

Coauthors: Yazmin G. Acosta Sanchez, Nataliya I. Kalashnykova


In this paper, a general multi-sector, multi-instrument model of financial flows and prices is developed, in which the utility function for each sector is assumed to be quadratic and constraints satisfy a certain accounting identity that appears in flow-of-funds accounts. Each sector uses conjectures of its influence upon the prices of instruments. The equilibrium conditions are first derived, and then the governing variational inequality is presented. Next, a criterion of consistency of the conjectures is derived, and a qualitative analysis of the model is conducted.


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