MATLink 1.1 is now released.
This version brings full compatibility with Mathematica 10. If you use Mathematica 10, please upgrade.
Also, a warning: on Linux & OS X MATLAB R2014a has a bug which prevents MATLink from working correctly. Please do not use this version of MATLAB with MATLink on Linux or OS X. R2013b works fine, and so will R2014b when it is released (probably this September).
Windows users can use R2014a without problems.
Can I use CVX in MATLAB through MATLink?
I am not familiar with CVX, so I do not know.
Things that might prevent you from using it:
Does it rely on callbacks to Mathematica? E.g. would you need to pass a function implemented in Mathematica to it? That is not supported at the moment.
Would it require transferring MATLAB objects (i.e. classes) between MATLAB and Mathematica? This isn't supported either, but structs do work (you can convert the class to a struct first). All major datatypes are supported except classes, function handles and certain rarely used integer types. (We can add support for these integer types on request).
Does it require a very large number of calls to MATLAB? There is an overhead to each call so this might be slow.
If none of these apply then you should be able to use MATLink with CVX.
Point 1. will eventually be dealt with in MATLink 2.x (not 2.0). Point 3: the overhead will be significantly reduced in MATLink 2.0. Point 2 might be partially dealt with in MATLink 2.0, but full support for bi-direction transfer of arbitrary classes is unlikely.
Now if only I had time to work on version 2 ... My job doesn't leave much time for it these days.