A Graph-based Decentralization Proposal for Convex Non Linear Separable Problems with Linear Constraints.

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Title:	A Graph-based Decentralization Proposal for Convex Non Linear Separable Problems with Linear Constraints.
Authors:	Cerda, Jaime¹ jcerda@umich.mx, Graff, Mario¹ mgraffg@dep.fie.umich.mx
Source:	Proceedings of the World Congress on Engineering & Computer Science 2013 Volume I. 2013, p1-5. 5p.
Subjects:	Nonlinear theories, Nonlinear programming, Constraints (Physics), Sparse matrices, Graph theory
Abstract:	This document proposes several decentralization approaches for the Newton step graph-based model for convex non linear separable problems with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLP model will grow in a non linear manner. When this happens, the sparse matrix representation is the path to follow. Furthermore, decentralization schemes are suitable to keep the problem from growing exponentially. In this work a graph based method to achieve this decentralization is proposed. To this end, we have chosen to weak the links, which are part of the graph, as an alternative. These links eventually will guide the solution process in this approach, which implies to weak the links which are coupling the problems in order to achieve such decentralization. A deeper analysis of these links is done which leads to its complete understanding. It will be seen that the main effect of the link weakening operation is to allow the computation of the exact gradient. However, the solution will be reinforced by taking into account the second order information provided by the linking structure. Finally, different decentralisation schemes are presented based on the previous analysis. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This document proposes several decentralization approaches for the Newton step graph-based model for convex non linear separable problems with linear constraints. The Newton step is well suited for this kind of problems, but when the problem size grows the NLP model will grow in a non linear manner. When this happens, the sparse matrix representation is the path to follow. Furthermore, decentralization schemes are suitable to keep the problem from growing exponentially. In this work a graph based method to achieve this decentralization is proposed. To this end, we have chosen to weak the links, which are part of the graph, as an alternative. These links eventually will guide the solution process in this approach, which implies to weak the links which are coupling the problems in order to achieve such decentralization. A deeper analysis of these links is done which leads to its complete understanding. It will be seen that the main effect of the link weakening operation is to allow the computation of the exact gradient. However, the solution will be reinforced by taking into account the second order information provided by the linking structure. Finally, different decentralisation schemes are presented based on the previous analysis. [ABSTRACT FROM AUTHOR]
ISBN:	9789881925237