Successive convex approximation is used in my algorithm

I believe your question two above is addressed by my answer to your question at Disciplined convex programming error: Cannot perform the operation: {real affine} .* {convex} .

I will presume your very convoluted code in your question immediately above has been superseded by your other code.

Please do not post the same thing, more or less, to multiple threads. It adds to confusion and messiness of the forum, and increases the effort required by volunteers (such as myself) to help you,