Convex optimization problem to quadratic programming problem
Briefly, have the following problem:
where is a linear function, , n is huge comparing to the size of x.
It is possible to write an equal Quadratic Programming problem, such as
which can be solved very efficiently with an appropriate numerical method.
Unfortunately in my particular case such conversion doesn't work: it adds a lot of new restrictions, and that appropriate numerical method doesn't converge.
I tried to figure out another equal QPP, which adds fewer new constraints, but nothing came across my mind. Is there another way?