Why should we prefer Yalmip to Matlab LMI Solver for Convex Optimisation

[Muhammad Yasir]

As far as I understand, Matlab LMI Solver tool may be used to solve convex optimization problem. Why should we prefer Yalmip to Matlab LMI Solver tool?

[Johan Löfberg]

You are talking  about different things.

You have the modelling language (YALMIP vs LMILAB language), and in my opinion the LMILAB modelling is absolutely horrible and obsolete. It is extremely cumbersome to model anything non-trivial. The whole reason YALMIP was developed some 20 years ago was the agony of doing anything advanced efficiently in LMILAB, and it is just as bad today.

You then have the solver (interfaced via YALMIP such as mosek, sedumi, etc, vs the solver in LMILAB). The solver in LMILAB is several decades old, and pretty inefficient on general problems. It is efficient on standard Lyapunov-ish LMI control problems, if modelled using the specific modelling constructs in LMILAB, but the model has to be really large and simple for this to be any kind of motivation for struggling with the modelling language LMILAB. The solver dos not have any constructs to exploit SOCP cones either, so it is a very limited solver compared to solvers sucas mosek,sedumi, sdpt3 when you start doing anything but vanilla control LMIs.

[Johan Löfberg]

...and important to remember, in YALMIP semidefinite programming is just a special case, so leaving that world is no problems, while in LMILAB you are only modelling simple LMI problems and doing something else requires you to switch tool completely.

[Muhammad Yasir]

Thank you for sharing your views on this matter.

What I have been able to understand is that Yalmip is a modeling tool that employs solvers like sdpt3, gurobi and sedumi etc. to solve the optimization problem.

Moreover, while trying to solve the convex optimization problem using Matlab LMI solver, I have found it quite cumbersome to model the problem for a solution through convex optimization. On the other hand, Yalmip seems very easy to understand and use for modeling and solving such a problem

Anyways, I am trying to develop my skills in using Yalmip