Do different versions of MATLAB need to install different versions of MOSEK solver? Does the MOSEK solver work without a license?Because my problem can not get the ideal result, I doubt whether it is the problem of the solver version.
You can have the same or many versions of MOSEK and the same or many versions of Matlab combined in various ways, it just depends on which path(s) you add in Matlab.
You can get a trial https://www.mosek.com/try/ or academic https://www.mosek.com/products/academic-licenses/ license for MOSEK