## convex optimization problem

Convex optimization problem:

The goal is to minimize,

$\sum{|y-x|^2}$,

such that,

a] K-L divergence between probability distributions for x and y, is maximum i.e. D(p(y)||q(x)) is maximum

b] $\sum{y} < \alpha$, where $\alpha$ is constant.

c] x,y < $\beta$

How can I approach this problem?

-
 Sorry if I gave the impression of imperative mood. I was trying to put it across in the format of a formal optimization problem. Edited accordingly. Thanks. – skypemesm Oct 30 2010 at 18:54 Could you provide an algebraic definition of K-L divergence in your case? It looks like you have an inner maximization problem there; I'm just wondering if the optimality conditions of that inner problem result in convex constraints. Otherwise it'd be a bilevel problem. – Gilead Oct 30 2010 at 21:16