I'm interested in multistage optimization problems. Are there any good R packages around to solve such problems over time? I'm not at all an expert in it, so maybe someone knows a good paper / lecture notes to start with? I know classical optimization (linear optimization, convex optimiziation etc) but I've never had to deal with optimization over time. Any reference, theoretical and regarding the implementation are very welcome. I know that this is a very general question, but this is due to my (not yet) attained knowledge. If further clarification is needed I'm happy to share thix. Many thanks in advance
EDIT
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. However the theory I'm looking for should give me ideas if it is optimal to solve at every time $l$ the subproblem (maximize $\sum_{i=1}^{n+1}r^l_ix^l_i$ under the corresponding constraints or is this not a good idea. I have heard / read that one could solve such kind of problem using stochastic programming, but still I'm interested in knowing how to subdivide (if possible) such kind of problems.