Can BFGS be used to minimise several functions at once?

Question

I have multiple objective functions which are related to several parameters. I want to minimise more than one objective functions using several parameters. Is it even possible using BFGS?

When I used L-BFGS to minimise one objective function using several parameters, it worked fine. However, I am unable to minimise multiple objective functions. At the moment, as my functions are just numbers, I've added all of the objective functions and their associated gradients in order to minimise my objective funtion. I'm unsure if that's the best way to approach this situation.

Any help would be much appreciated.

Kind regards,

Mo

Answer 1

Not by itself, no. The optimal solutions of multiobjective optimization problems are Pareto optimal solutions. Multiobjective optimization problems have their own specialized algorithms, as can be seen in the corresponding Wikipedia article. Some of these methods construct surrogate single objective optimization problems, which could be solved with L-BFGS; other methods do not construct surrogate problems (such as particle swarm optimization). If you're interested in solving multiobjective optimization problems, I suggest you search that literature for methods that might be appropriate for your problem.