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: | Rustem Ber, Fasca Nuno P, Saraiva Pedro M, Pistikopoulos Efstratios N |
Keywords: | programming: parametric |
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.