The pre-condition is a>b, so I can prove that the objective function is concave. The challenge is how to process constraint (1), since both sides of (1) are concave. I feel so close to the right answer, but still can not find a good way to it. Does anyone have a clue? Many thanks!

# Does anyone know how to transform this problem into a convex one?

Nothing at

seems useful.

Is there a good reason x_3=Q is not optimal.

Thank you, Erling!

If constraint (1) is inactive, we can always decrease x_{3} until (1) is avtive. If constraint (3) is inactive, we can always increase x_{4} until (3) is active. So we have at most two equations. Those are what I can think of.