A Global Parametric Programming Optimisation Strategy for Multilevel Problems
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In this paper, we outline the foundation of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems based on our recent developments in multiparametric programming theory. The core idea is to recast each optimisation subproblem in the multilevel hierarchy as a multiparametric programming problem and the transform the multilevel problem into a single-level optimisation problem. 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. 2006 Elsevier B.V. All rights reserved.