As per the model coordination described in literature the optimization problem in the second level (or primal problem) is an unconstrained one (there may be some bound constraints on the coordinating decision variable). Only coordinating decision variables are calculated in the second level ( the other variables are calculated in the sub levels and appears as parameters in the second level). As, there are no constraints in the second level the coordinating variables will always assume the value of lower bounds for minimization problems and upper bounds for maximization problems. Without the constraints (that will reflect the subsystems behavior) I am unsure, how the optimizer will guide the decision variables to its optimal value. I have simulated several problems and in all cases the decision variables are reaching the bounds. To be noted in all my case studies coordinating variables does not have a constraint dedicated for it (except bounds) in the second level. So, logically there is no incentive to push the variable towards it's optimum value. But the literature I consulted claims (but does not explain how or why) that the correct result can be achieved using the above mentioned methods for these cases also.
Dear Shamik,
Among the researchers who have noticed themselves in this field is the name of N. Sadati and there are others, here are attached files related to this topic as well as links.In studying this documentation, I think you could answer your question.
- Proceedings of the Tenth Power Systems Computation Conference
https://books.google.dz/books?isbn=1483101045
- Adaptive Resource Management and Scheduling for Cloud Computing: ...
https://books.google.dz/books?isbn=3319134647
- Power System Optimization: Large-scale Complex Systems Approaches
https://books.google.dz/books?isbn=1118724747
- New hierarchical method for path planning of large-scale robots
www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0327...
- European Control Conference 1991: Volume 3
https://books.google.dz/books?isbn=2866012828
Best regards
The outline that you describe has to do with the theory and practice of the multilevel optimization. I am the author of an analysis and synthesis methodology of engineering systems, with a significant quantity of applications. In the worki am attaching you can find the basic aproach developed with some applications. If it is of your interest, we could in the future to speak about details.
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