If you have an efficient mixed-integer SOCP solver installed (such as gurobi, cplex or mosek), you can for instance add combinatorial structures, such as a cardinality constraint on your positions solvesdp(, Objective) Hence, the following problem derives the result in the paper and solves the problem w = sdpvar(n,1) Robust = Īctually, YALMIP has a built-in framework for deriving these kind of robust models automagically. Otherwise, it will probably use fmincon n = 10 If you have an efficient second-order cone programming solver installed, it will use that. To begin with, solve the problem as manually derived above.
MATLAB NOT EQUAL CODE
It could also be interesting to know that the problem easily generalizes to other norm-balls on the uncertainty.įor fun, here is some experimental code in the MATLAB Toolbox YALMIP Although fmincon most likely will work, it is not really the best tool for the task, since this is a very particular problem class for which there are dedicated extremly efficient solvers. You have $r_p = \alpha + rU $ where the uncertainty $U$ is known to satisfy $U^TU \leq 1$ and your radius happen to be parametrized as $\kappa \left|\alpha\right|$.Īfter performing the minimization over the uncertainty, i.e, eliminating the for-all operator in the uncertain constraint, it boils down to a standard quadratic problem with a convex norm-constraint.
![matlab not equal matlab not equal](https://online.fliphtml5.com/lnym/dsql/files/large/1202.jpg)
Just adding to the answers above, untangling the notation bit to put it in standard robust optimization format.
MATLAB NOT EQUAL HOW TO
This can be done using global variables (the old fashioned way) or using anonymous functions (the way that the Mathworks now recommends.) There are instructions on how to do this with an example in "help fmincon" One slightly tricky issue here is how to get the parameters $\chi$, $\alpha$, and $\Sigma$ into these functions. To solve this problem using fmincon, you need to define a MATLAB function for objective and another MATLAB function for the nonlinear constraint. Note that I had to multiply the greater than or equal to constraint by negative one to turn it into a less than or equal to constraint.
![matlab not equal matlab not equal](https://0.academia-photos.com/attachment_thumbnails/36049972/mini_magick20190310-31460-oc4c15.png)
You haven't said it, but I wouldn't be surprised if you also wanted to add the constraint $\omega \geq 0$. Based on the discussion in comments on your original question, it appears that your problem can be formulated in the form required by fmincon as