From the research on lossless convexification or the exact convex relaxation technique, it is evident that this technique heavily relies on specific optimal control problems. I would like to ask under what conditions a constraint can be convexified losslessly. Or, how can a constraint be convexified losslessly?

For example, consider the equality constraint x^2 + y^2 = 1. If x and y are not influenced by other constraints, this constraint can be relaxed to x^2 + y^2