A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

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Article ID: iaor200971049
Country: Germany
Volume: 6
Issue: 4
Start Page Number: 377
End Page Number: 397
Publication Date: Oct 2009
Journal: Computational Management Science
Authors: , , ,
Keywords: programming: parametric
Abstract:

In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.

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