how to avoid the status is ill posed, how to choose the initialize the problem with a feasible point?
Your problem will not become less ill posed by changing the starting point. In any case that is not even possible in CVX to the best of my knowledge.
You should take a deep look at your model which most likely is not well posed.
@Erling correctly answered your question if you are talking about providing a starting point to the solver called by CVX.
However, if you are talking about choice of starting point for a higher level algorithm you wrote which calls CVX to solve a sequence of convex optimization problems, my answer at The value is cycling in the two value addresses that.