How to choose a Local optimization algorithm

I have to find the global minimum of a scalar function of 22 variables. These variables must stay inside bounds and some of the variables are subject to linear constraints. I have used Genetic Algorithm to find a solution of the problem and now I would like to use this solution as starting point for a local optimization algorithm. I have seen that there are a lot of different methods. What is the best method suited for my problem? And could you explain me briefly how these algorithms work? Thank you.

Answer 1

[Matt J]

You probably will want to use quadprog or lsqlin if your problem is quadratic. Otherwise, fmincon with the sqp algorithm if the problem is smooth, nonquadratic. Algorithm descriptions are available online, e.g.,

http://www.mathworks.com/help/optim/ug/quadratic-programming-algorithms.html#brnox76

http://www.mathworks.com/help/optim/ug/constrained-nonlinear-optimization-algorithms.html

If the problem is not smooth, you have probably already done as much as you can do with GA.

But your question begs another question. Why do you now want to use a local optimization algorithm when you have already optimized globally?