Newton's method for linear inequality systems

Article Abstract:

Modifications in the Newton algorithm developed by Madsen and Nielsen (1990) enabled the algorithm to better resolve the solution of linear inequality systems. The algorithm was improved in terms of its generation of the absolute level of infeasibility. The improved Newton's algorithm was shown to be superior to the library routine LSSOL from Stanford University Systems Optimization Laboratory, since the algorithm showed a slow growth rate in the number of iterations even as the problem size increases and a constant rate of refactorizations despite the increasing problem size.

Operations Research, Mathematical optimization, Optimization theory

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On linear inequality systems without strongly redundant constraints

Article Abstract:

Redundancy is a computational constraint to the solution of the size reduction problem in linear programming theory. However, linear inequality systems have been developed that do not hold strongly redundant constraint sets. Such conditions are generated by sharp constraint vectors that define a maximum-closed polyhedral cone. Construction of the finite generating set for the polyhedral cone is limited to a description of the vectors for any set.

Inequalities (Mathematics)

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Decomposition and iterative aggregation in hierarchical and decentralized planning structures

Article Abstract:

Iterative aggregation and disaggregation within the organizational and planning context is analyzed. Basic decomposition approaches are compared to basic aggregation methods which emphasize the information flow between different organizational levels. It is shown that the structure of the organizational problem can be simplified to a communication process where information is exchanged between different levels.

Decentralization (Management), Decomposition method

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