I am more and more getting the idea that i need to solve my optimization problem at 2 levels, to find the optimal solution, because of its dimensionality.
The results of the lower level optimization problem is used to guide the top level optimization problem towards the optimal solution.
The top level must set/ search additional parameters that guide the lower level optimization.
It is a nonconvex nonlinear optimization problem
Sure. Look up multilevel optimization. Bilevel optimization is particularly common.
Sure. Sometimes, the given optimization problem can be simplified considerably using such a multilevel optimization approach.
For example, a nonlinear and nonconvex optimization problem has been decomposed into a scalar root finding problem and a convex optimization problem in Article Optimal stability polynomials for numerical integration of i...
,which can be solved more easily using bisection and a convex solver.
Have you tried to use Nash equilibrium approach for formulation of your problem?
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