Find minimizer of convex function with linear constraint

1

Hi, I am new to CVX. I am wondering can I use CVX to find the minimizer of the following problem.
min ||x-x_{0}||
subject to Ax=b
where A is a large-scaled sparse matrix and b is a suitable vector.
Thanks a lot for any help in advance.

2

Have you read the CVX Users’ Guide http://cvxr.com/cvx/doc/ ? This forum presupposes you have done so. This problem should be trivial to enter almost exactly as written.

3

Thanks a lot for your reply.
I am sorry that I just started to read the User’s Guide. I tried to do the implementation in Matlab using the syntax as what I stated the problem. I only got the minimal function value. But What is important for me is to obtain the minimizer, the point x, attaining the minimum of the function value. I will carefully read the user’s guide these days. Do you mind to tell me whether I can use the CVX to obtain the minimizer x in my problem above?

4

Yes. if you declare x as a vector variable
variable x(n)
then after CVX complet4es, presuming it reports status as solved, x will then be a regular MATLAB numerical variable, populated with the optimal value of x from the optimization problem. You can then do with it whatever you want, as allowed by MATLAB, with no further regard to CVX or its rules.

5

Dear Mark,

I got it. I appreciate so much for your patience and kind help. I will read the User’s guide carefully these days. Thanks a lot again. Have a great day.