I'm interested in multistage optimization problems.
Let's take for example the following paper, there we have a optimization problem of the form:
$$\max \sum_{i=1}^{n+1}r^L_ix_i^L$$
such that
$$ x^l_i=r^{l-1}_i x_i^{l-1}-y_i^l+z^l_i,\hspace{2pt} i=1,\dots n,l=1,\dots,L$$ $$ x^l_i=r^{l-1}_{n+1} x_{n+1}^{l-1}+\sum_{i=1}^n(1-\mu^l_i)y_i^l-\sum_{i=1}^n(1+\nu_i^l)z^l_i$$ $$y^l_i\ge 0,\hspace{2pt} i=1,\dots n,l=1,\dots,L$$ $$x^l_i\ge 0,\hspace{2pt} i=1,\dots n,l=1,\dots,L$$ $$z^l_i\ge 0,\hspace{2pt} i=1,\dots n,l=1,\dots,L$$ where some $x_i^l$ is the value (in dollar) of an asset $i$ at time $l$, $r_i^l$ is the asset return, $y^l_i$ and $z^l_i$ are the amount of asset sold and bought. $\mu^l_i $ and $\nu_i^l$ have also economical interpretation, but are not that important for the question. Assuming everthing is deterministic, we can solve this problem using interior points / simplex method since it is an "simple" LP. On the other hand I think one could solve this via dynamic programming approach. What would be the advantage or disadvantage of this? Does the situation change if I apply a "utility function" $f$(convex let's say), i.e.
$$\max \sum_{i=1}^{n+1}f(r^L_ix_i^L)$$
Many thanks for the insights.
Usually dynamic programming methods (if applicable to the problem - in your question its applicable) are faster than LP methods.