all, I've tried to find an answer to this question and have come across some related threads but nothing I was able to apply to my problem given my relative lack of experience in this arena.
I basically have a constrained minimization problem using both inequality and equality constraints. I will have more variables (~10) than equality constraints (6), so generally speaking there will be an infinite number of solutions to the system. The wrinkle is that I want my solution vector to have as many zero elements as possible, or more precisely I want to minimize the number of non-zero elements. The real-world application is that each variable represents a trade in a portfolio, so I want to hit my "targets" in the portfolio with the fewest number of necessary trades.
My initial approach was to use the fmincon function in Matlab with the objective function as
But this approach results in a spurious solution even for the most basic test example I could come up with. Is a problem like this solvable in Matlab? Any help would be much appreciated, I'm really at an impasse. Thanks.