I have to two expressions: (||x-ay||^4)/a^3 and (||x-ay||^3)/a^2, where the real vector x and the nonnegative scalar a are the optimized variables. The real vector y is known.
These two expressions are joint convex in (x, a). How can I express them in the acceptable forms?
For the second one, How to reformulate this in a CVX way: Cube over Square - #31 by Mark_L_Stone , but you’ll need to restrict
a > 0,which the geo_mean
formulation automatically does, because the expression is concave fora < 0`;
For the first one, add an extra
a as an argument of
geo_mean in the above link. Similarly, you’ll need to restrict
a > 0, which the geo_mean` formulation automatically does.
The provided link ultimately points back to @Erling 's formulation.
Hi, Mark. It works. Thanks for your answer!