Journal
COMPUTATIONAL MANAGEMENT SCIENCE
Volume 6, Issue 4, Pages 377-397Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s10287-007-0062-z
Keywords
Hierarchical decision making; Multilevel programming; Multi-parametric programming; Discrete-time systems; Closed-loop optimal control
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Funding
- EPSRC [GR/T02560/01]
- Marie Curie European Project PRISM [MRTN-CT-2004-512233]
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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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