I will continue the notation I used in previous post.
The convex optimization problems are defined as follows:
Here, for notational brevity, the convex optimization problems can be expressed in the following way:
where
First-order condition for optimality.
For a convex problem above, if if differentiable, a feasible point is optimal if and only if for all .
Take Home Message
All feasible directions from are aligned with increasing gradient .
Special Case
When (unconstrained optimization), then optimality condition reduces to familiar .