it is best to have good scaling, but if the scaling isn’t great, mosek might handle it better than sdpt3, sedumi, or ecos.
Read section 2.2.6 of 2 Linear optimization — MOSEK Modeling Cookbook 3.3.0 .
Read Scaling and numerical stability
Per Support — CVX Users' Guide
Watch for scaling issues.
Scaling issues are the most vexing problems for numerical solvers to deal with. Solvers will often re-scale the problem to reduce the dynamic range of the numerical coefficients, but doing so sometimes leads to undesirable effects on the solution. It is better to avoid scaling issues during the modeling process. Don’t mix values of wildly different magnitudes, such as 1e-3 and 1e20. Even better, try to avoid any numerical values (both in fixed parameters and likely values of the variables) that exceed 1e8 in absolute value.