  Let $P$ be a set of $n$ points in $\mathbb{R}^2$. For a given positive
integer $w<n$, our objective is to find a set $C \subset P$ of points, such
that $CH(P\setminus C)$ has the smallest number of vertices and $C$ has at most
$n-w$ points. We discuss the $O(wn^3)$ time dynamic programming algorithm for
monotone decomposable functions (MDF) introduced for finding a class of optimal
convex $w$-gons, with vertices chosen from $P$, and improve it to $O(n^3 \log
w)$ time, which gives an improvement to the existing algorithm for MDFs if
their input is a convex polygon.
