Algorithm choice in numerically solving large constrained nonlinear optimization
I am wondering about algorithm choice in solving numerically a large constrained nonlinear optimization problem.
The problem has ~1 million variables and ~500,000 nonlinear constraints. You are allowed infinite processors (for parallel computing), and a sample solution is known to start the optimization. You can also assume that the first and second derivatives of the constraint functions are known.
The problem can be stated:
Minimize f(x) over x, subject to the constraints h(x)=0, g(x) <= 0, and lb<x<ub
This means that x is a vector of variables limited with lower and upper bounds, and subject to some number of constraints.
I have explored many types of algorithms, but do not have a conclusive answer for which is the best for this type of problem (large-scale, known derivatives, etc). Any ideas for a good, parallelizable algorithm?