I want to write code for solve this system, but I don’t know: A.DELTX=0 A’DELTAY+QDELTAX+DELTAS=0 XDELTAS+ SDELTAX=T-X
Where unknowns are DELTAX, DELTAS are nn symmetric matrices, DELTAY is mn matrix, A is mn matrix,Q is nn matrix, and semidefinite and symmetric.
Thanks for your attention.

Please use the formatting instructions on the right-hand side of the page to clean up your question. It is unfortunately indecipherable. But in general, no, CVX cannot solve quadratic SDPs, unless you can translate them to linear SDPs.

I want to write code for solve this system, but I don’t know: A.DELTX=0 A’DELTAY+QDELTAX+DELTAS=0 XDELTAS+ SDELTAX=T-X
Where unknowns are DELTAX, DELTAS are nn symmetric matrices, DELTAY is mn matrix, A is mn matrix,Q is nn matrix, and semidefinite and symmetric.
Thanks for your attention.

I have deleted this post. Unfortunately your edit made things even more difficult to understand. Again, please look at the “Formatting basics” section on the right-hand side, particularly the sections on Equations and Source code.