The BLAS subroutine library is a well-defined standard for performing dense matrix operations such as matrix times matrix operations. Usually hardware vendors provide highly optimized BLAS libraries. MOSEK does not employ a BLAS library for the following reasons:
Nearly all matrix operations used by MOSEK are sparse — switching these to dense operations would make MOSEK significantly slower.
BLAS libraries usually adds lot of external dependencies on other libraries which can cause problems when MOSEK is linked with a customer's applications. In other words, the more third party libraries we employ the more likely our customers we will see compatibility problems.
Using a BLAS library adds a source of bugs to MOSEK. Getting bugs fixed in third party libraries usually takes significantly longer than fixing bugs in our own code.
We have found that in general the complications outweighs the benefits of using a third party BLAS library.