0

I know that for $x,a,b\ge0$; ${Q({a_i} + {b_i}\sqrt x )}^2$ holds convexity because the $Q$ function holds the convexity (monotonicity) . I dont know how should I approach to prove

$$\log \left( \sum_{i = 1}^N \varepsilon_i\left( Q(a_i + b_i\sqrt x ) \right) ^2 \right)$$

is convex for $x \ge 0$.

Rodrigo de Azevedo
  • 1
hasan
  • 137
  • 1
  • 9
  • If $N=1$, $Q(x)=x$, $a=0$, $b=1$, $\epsilon=1$ then the new function is $\log{x}$ hence not convex. – Michal Adamaszek Oct 25 '19 at 06:16
  • Thanks you for your reply. As logx is concave so I can say the function I mentioned in the above section is strictly concave. Is it straight forward like that? – hasan Oct 26 '19 at 07:47
  • I don't think you can conclude anything for such a general Q. What exactly do you assume about Q? You are not being very precise about it. – Michal Adamaszek Oct 26 '19 at 21:49

0 Answers0