Some Constraints are Violated in CVX

1

I am using CVX to solve a certain constrained optimization problem using DC programming approach. However, the CVX solution doesn’t satisfy all the constraints.

Can I force CVX to satisfy all constraints? If yes, How can I do that? If no, which solver do you recommend me?

Thanks in advance.

2

You’re going to have to provide specifics. How far are the constraints violated? Frankly, with any numerical solver, you have to expect, and account for, small violations in all active constraints.

3

They are violated by large values (about 30% to 40% violation of inequality constraints).

-The objective function contain sum of log terms. I knew that CVX approximate it using Successive approximation method. Is this the reason of violation??

-The dimension of decision vector is very large (about 3000 variables), but 80% of the variables are known to be zero a priori, and they are constrained to be zeros. Does decreasing the problem size by removing the zero variables implies better solution accuracy in CVX??

Thanks in advance

4

Yes, I suspect logs are the problem. However, if you have a sum(log(x)) objective, just maximize geo_mean(x) instead. It’s equivalent, and avoids successive approximation. Nevertheless, if you can supply a self-contained example to http://support.cvxr.com, we can take a look.

5

Thanks Dr.Grant. I appreciate your quick response.