Hello,
I want to solve this problem with CVX. But the objective function is concave. Please guide me how to convex it.
My objective function is max min of:
What are the optimization variables? is b(i) <= 0? I will presume so.
If one of P and ho is the only optimization variable, R(i) is concave, so min(R) is concave and can be maximized, almost as written.
If one of the variables in the denominator is the optimization variable then (leaving aside the squaring,. and assuming the square is defined as the CVX variable, and the constraints allow that to be done, and that P*h0 > 0,), then log(...) is convex; and therefore min(R) is neither convex nor concave, and so can’t b e used in CVX.
Please carefully read Why isn't CVX accepting my model? READ THIS FIRST! .
It is generally a fool’s errand (bad idea) to attempt to convexify a concave expression. If you really have a non-convex problem, use a non-convex optimizer, such as available under YALMIP.