$.
The function inside the $\arg \min$ is strictly convex if and only if
$\lambda_h$ is not null. This asymptotic configuration may arise due to
-the definition of $\lambda_i$. Worth, in this case, the function is
+the definition of $\lambda_h$. Worth, in this case, the function is
strictly decreasing and the minimal value is obtained when $p$ is the infinity.
To prevent this configuration, we replace the objective function given
In this equation we have first introduced new regularisation factors
(namely $\delta_x$, $\delta_r$, and $\delta_p$)
instead of the sole $\delta$.
-This allows to further study the influence of each modification separately.
+This allows to further separately study the influence of each factor.
Next, the introduction of the rational exponent is motivated by the goal of
providing a strictly convex function.
\begin{array}{rcl}
f'(p) &=& -2/3.v_h.\dfrac{\ln(\sigma^2/D_h)}{\gamma p^{5/3}} + \lambda_h +
8/3.\delta_p p^{5/3} \\
-&& \dfrac {8/3.\delta_p p^{10/3} + \lambda_h p^{5/3} -2/3.v_h\ln(\sigma^2/D_h) }{p^{5/3}}
+& = & \dfrac {8/3\gamma.\delta_p p^{10/3} + \lambda_h p^{5/3} -2/3.v_h\ln(\sigma^2/D_h) }{p^{5/3}}
\end{array}
$$
which is positive if and only if the numerator is.
-Provided $p^{5/3}$ is replaced by $P$, we have a quadratic function which is strictly convex, for any value of $\lambda_h$.
+Provided $p^{5/3}$ is replaced by $P$, we have a quadratic function
+which is strictly convex, for any value of $\lambda_h$ since the discriminant
+is positive.
\ No newline at end of file
