Increment of the objective function and optimality criterion for one non-homogeneous network flow programming problem

For an linear non-homogeneous flow programming problem with additional constraints of general kind are obtained the increment of the objective function using properties of the problem and principles of decomposition of a support. Optimality conditions are received

Algorithms for construction of optimal and suboptimal solutions in network optimization problems

For a distributive flow programming optimization problem of a special structure direct and dual algorithms are constructed. These algorithms are based on a research of the theoretical and graph properties of the solution space bases. Optimality conditions are received, that allow to calculate a part of the components of the Lagrange vector. Algorithms that decompose calculation systems for pseudo-plans of the problem are presented. Suitable directions for change of the dual criterion function are constructed

Decomposition of the network support for one non-homogeneous network flow programming problem

We consider one extremal linear non-homogeneous problem of flow programming with additional constraints of general kind. We use the network properties of the non-homogeneous problem for the decomposition of a network support into trees and cyclic parts

Linear-fractional programming: problems of optimization of inhomogeneous flows in the generalized networks

Полный текст статьи можно найти по адресу: http://ijpam.eu/contents/2013-82-2/9/index.htmlHere we consider the linear-fractional non-homogeneous flow programming optimization problem with additional constraints of general kind. We obtain the increment of the objective function using network properties of the problem and principles of decomposition of a support. In the received formulas for calculation of reduced costs only the part of system of potentials is used

Underdetermined linear systems in the sensor location problem

We consider underdetermined linear systems and characteristics of optimal solutions in the sensor location problem

Sensor Location Problem for a Multigraph

MSC 2010: 05C50, 15A03, 15A06, 65K05, 90C08, 90C35We introduce sparse linear underdetermined systems with embedded network structure. Their structure is inherited from the non-homogeneous network ow programming problems with nodes of variable intensities. One of the new applications of the researched underdetermined systems is the sensor location problem (SLP) for a multigraph. That is the location of the minimum number of sensors in the nodes of the multigraph, in order to determine the arcs ow volume and variable intensities of nodes for the whole multigraph. Research of the rank of the sparse matrix is based on the constructive theory of decomposition of sparse linear systems

Solution of large linear systems with embedded network structure for a non-homogeneous network flow programming problem

In the paper we consider the linear underdetermined system of a special type is considered. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a large sparse submatrix representing the embedded network structure. A direct method for finding solutions of the system is developed. The algorithm is based on the theoretic-graph specificities for the structure of the support and properties of the basis of a solution space of a homogeneous system. One of the key steps is decomposition of the system. A simple example is regarded at the end of the paper