Dear Muhammad,

It seems to me that the wording of your question is not clear enough, it is the dependence on structural system level or it is an optimization problem with multiple criteria. Every time I allow myself to suggest some references attached.

Best regards

According to the nature of the subproblems dependencies you can look for the correponding algorithm.

if the subproblems you defined are  hierarchical planning problems, than may be you can look in algorithms for bi-level or multilevel optimization.

This book will be usefull:

http://www.springer.com/us/book/9783642378379

There is also some references about the multilevel optimization in the book.

Bests

Dear Mohamed,

The problem is an optimization problem and the only criteria is to minimize the cost function which itself is very complex.

Dear Muhammad,

After your second comment I think I understand your problem.

For this here is a bibliography attached supplement that I hope will help you in your task

Best regards

try to use "benders decomposition optimization"

If your problem is unconstrained N. Z. Shor's method of generalized gradient descent with space dilation in the direction of the difference of two successive subgradients (the so-called r-algorithm) will be useful.

You mention "subproblems" - how are they defined in terms of the "full" problem? Is there some problem structure that can be utilized, such as a separability of some subvectors in the objective function? As it is, your explanation about the problem properties is rather limited.

you may try the "bender decomposition algorithm"