I want to search for the optimum solution to a Lambert Problem to find the optimum transfer orbit between two arbitrary orbits. This problem has two independent variables which is the time of departure and time of arrival (those are then fed into the actual Lambert Solver to find the cost of the transfer which is the objective function to be minimized).
There are numerous complications to the problem, but assume the orbits are roughly circular and coplanar so that the optimum 2-impulse transfer orbit will be roughly a Hohmann orbit, etc. Consider the space of problems to be limited to ones that are fairly reasonable. There are various complications related to finding global minimum vs. local minimum which is not the point of this question, either.
I'd just like to know which algorithm is likely to produce better convergence for this kind of problem - Conjugate Gradient, Limited Memory Broyden–Fletcher–Goldfarb–Shanno, or Levenburg-Marquardt? If you have those three algorithms to pick off the shelf, which is the first choice to try?
[ And I'm asking because my first guess was Levenburg-Marquardt and it appears to be having convergence difficulties. I'm also using C# and alglib.net's optimization toolkit, any algorithm in there is also fair game ]