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

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 optimisa...

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Bibliographic Details
Published in:Computational management science Vol. 6; no. 4; pp. 377 - 397
Main Authors: Faísca, Nuno P., Saraiva, Pedro M., Rustem, Berç, Pistikopoulos, Efstratios N.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.10.2009
Springer Nature B.V
Subjects:
Algorithms
Business and Management
Control theory
Decision making
Equilibrium
Game theory
Mathematical programming
Operations Research/Decision Theory
Optimization
Original Paper
Studies
Discrete-time systems
Multi-parametric programming
Multilevel programming
Hierarchical decision making
Closed-loop optimal control
ISSN:1619-697X, 1619-6988
Online Access:Get full text
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Summary: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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ISSN:1619-697X
1619-6988
DOI:10.1007/s10287-007-0062-z