Quadprog - variable values zero or higher than particular value

Hello,

I am trying to use quadprog in Matlab to solve quadratic problem with particular constraints. Here are they:

1.) x has to be weights vector, so sum of x has to be 1. This includes also constraint, that all values of x have to be from interval (0,1), including 0

2.) x * vector1 = particular value. (vector1 is known, and particular value is set in constraint)

Everything works great and setting constraints wasn't that hard.... but my vector x contains approximately 6000 variables. That makes values of almost all of those variables to be less than 10^-4. I would like to make them zero or higher than some value (for example 0.01). Is it possible? Right now, if I extract 20 most biggest values and make new weight vector depending on sum of their values from result of quadprog, second constraint is not satisfied anymore, there is really big difference. Even the minimum of 1/2*x*H*x is totally bad. Is there any other way to do what i need?

Thanks a lot :)

Answer 1

[Alan Weiss]

I believe that something like your requirement is satisfied in the latest release Mixed-Integer Quadratic Programming Portfolio Optimization: Problem-Based. Or, for earlier toolbox versions, see Mixed-Integer Quadratic Programming Portfolio Optimization: Solver-Based.

Alan Weiss

MATLAB mathematical toolbox documentation

[Miroslav Strba]

Thank you very much. It looks very good :)

Answer 2

[Matt J]

Well, you can't do it with quadprog. The additional constraints can be handled by making this a mixed integer optimization, i.e., by reformulating your original variables x(i) as

x(i)=b(i)*y(i), y(i)>L

where b(i) are binary variables and y(i) are continuous variables with lower bound L=1e-4. The ga() solver in the Global Optimization Toolbox will let you specify such a problem, but I suspect the solver may just attack it like one big combinatoric optimization.