# 20th GAMM-Seminar Leipzig on Numerical Methods for Non-Local Operators

#### Max-Planck-Institute for Mathematics in the Sciences Inselstr. 22-26, D-04103 Leipzig Phone: +49.341.9959.752, Fax: +49.341.9959.999

 Homepage 20th GAMM-Seminar January, 22th-24th, 2004 Winterschool on hierarchical matrices Announcement Registration Participants Programme Abstracts Proceedings Archive All seminars All proceedings

 Abstract Seilkhan Boranbayev Previous Contents Next The Method of Solution of Optimization Network Mathematical Model Seilkhan Boranbayev (University Kazakhstan) The mathematical model of M graph can be presented as follows: where - are the prescribed states of input nodes, - is the vector characterizing the state of , , - is the vector of , , - is the vector characterizing the state of controlling objects , . Thus, the state of the node depends on the state of the nodes , and , , and is as well defined by the values of its parameters . - is a function vector and generally it is non-linear with reference to its parameters. Suppose that the Jacobian vector of function does not degenerate at the assumed values of controlling actions, consequently, states of , , nodes are not defined uniquely under given , , and . Denote via the set of vertices the conditions of which are defined by recurrent relations (i.e. these are the vertices which do not require solution of some subsystem equations (1) - (2) for the definition of their states). Lemma 1. The set of a graph's inputs is defined by recurrent relations, i.e. . Lemma 2. It follows from that and vice versa. Lemma 3. It follows from that and consequently, . Theorem 1. Vertex is incalculable recurrently, if it is possible to find a loop cycle containing this vertex. Previous Contents Next

Last updated:
30.11.2004 Impressum

 Concept, Design and Realisation Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)