Hello Soufyan:

the names "interior-point" and "barrier" are often synonymous when referring to optkmizaiotn algorithms, although I cannot guarantee that this is exactly what Matlab's solver is using.

If you are solving QP with Gurobi's barrier, you may want to look into

https://www.gurobi.com/documentation/9.0/refman/barqcpconvtol.html

as this parameter is used to determine the convergence criterion for our barrier.

For models where the data structures are sparse, it is often (very) advantageous to specify those as such, without the artificial step of making a full matrix filled with many 0's; indeed, linear algebra --a driving engine, so to speak-- behind the barrier is often more efficient with sparse matrices.

Hope this helps,

Hello Yuriy,

I don't really understand the last sentence of your answer: ''indeed, linear algebra --a driving engine, so to speak-- behind the barrier is often more efficient with sparse matrices.''

Could you elaborate more on this?

Furthermore, if I understand your answer correctly the data structures that Gurobi uses, are sparse. And due to that, it can handle sparse matrices more easy.

Regards,

At every iteration of the barrier one solves a system of linear equations, and this is often the most expensive part.

>> the data structures that Gurobi uses, are sparse

yes, you can think of it this way.

Hope this helps.