Which optimization tool should be used for solving my convex optimization problem?

My optimization problem is convex optimization problem and it is given as follows:

The objective function is given as

And constraints are

The final optimization problem is given as follows:

It is already verify that above optimization probelm is convex . I am using CVX tool to solve the above problem, but not giving accurate values (means that it is solving the problem).

Please suggest proper tool to write a MATLAB code to get the oprimal power values.

In some research papers , authors were saying that Interior point methods can be utilized. How Can I use this in MATLAB to finish above optimization problem?

Should I use CVX tool or any optimization methods to complete the solution for the given formulated problem?

Thanks in Advance!

[Torsten]

What do you mean by "CVX is not giving accurate values" ? Do you know the solution of your optimization problem ?

I don't think you have a big choice in the solvers you could use. Try "fmincon".

[KAGANA SARATH]

I do not know the solution of my optimization problem. My point is that eventhough the formulated optimization problem is convex in nature and have used CVX tool in implementing it.

Optimal power values are mostly zeros (For a K number of users), First K-1 users are almostly zeros and some power is given to the last user.

In this way, some undesired results and infeasibility is also the problem while solving the problem.

What about linprog?

[Torsten]

What about linprog?

Your objective doesn't look linear in p.

Here is a list of solvers available for optimization. Choose the one that best fits your problem class.

https://plato.asu.edu/guide.html

[KAGANA SARATH]

Yes it is not a linear but it is a convex problem.

In the list given, I am using CVX tool with MOSEK solver, But there is a convergence problem using this tool.

Hence, I am looking for another tool like 'fmincon'.

Sir, Can I use 'fmincon' to solve above problem ? Because, this problem includes optimization variables of vectors and complex in nature (How to give initial feasible points for the problem ).

[Torsten]

In the list given, I am using CVX tool with MOSEK solver, But there is a convergence problem using this tool.

You should first be optimistic about the solver used and search for the problem/error in your problem formulation/coding.

Answer 1

[William Rose]

@KAGANA SARATH,

I agree with @Torsten: try fmincon. It allows you to specify linear and nonlinear equality constraints and inequality constraints. The default algoritrhm is interior point method, but you can specify a different algorithm with optimoptions .

[KAGANA SARATH]

I think all are inequality constraints with respect to power 'p'

Answer 2

[Matt J]

If, as you seem to, you have a non-quadratic (and therefore also nonlinear) convex objective function, then you must use fmincon, regardless of the convexity or non-convexity of your constraints. There is no other solver in the Optimization Toolbox that will handle constrained non-quadratic minimization (except maybe fminimax, but you don't have a minimax problem).

[KAGANA SARATH]

I will follow your suggestions regarding the optimization toolbox. As I mentioned earlier, already used CVX tool with MOSEK solver.

There are two cases here:

1. When path loss at reference distance C0 = -30 db, the CVX is unable to solve the problem for lower powers (-30dBm to 30dBm) and works for higher powers but not desirable results.
2. When path loss at reference distance C0 = -10 db, CVX works for lower power values but not higher powers.

I am unable to decide this scenario, how it is working for specific path loss values (Related large scale fading). If I use fmincon, can I reolsve this issue? Please guide me in this matter.

Another thing is that CVX will not take initial feasible points in the process. If so, that feasible point may lead to optimal solution in the future iterations. As per my knowledge, fmincon will have this initial feasibility facility so that we can have feasible point as optimal values even if it is not working properly.