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](http://www.google.ch/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCEQFjAA&url=http%3A%2F%2Fwww2.isye.gatech.edu%2F~nemirovs%2Frob_portf.pdf&ei=OtX0U8OfI8jOOaqpgeAB&usg=AFQjCNHkJmuyt88kzk85A2cWTVYdH2vPxQ), 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.