Hi all,I'm trying to implement a little software to optimize portfolios using different constraints : either minimizing CVaR with a constraint on the global expected return, or maximizing the expected return with constraints on CVaR.Currently, I'm solving the Linear Programming problem given in this article : http://www.webpondo.org/ariascos/Files/ ... varfen.pdf . It works fine for a limited number of MC scenarios (~1000 scenarios). For a larger number of scenarios, there is memory issue in my symplex algorithm.So now I'm trying to implement the algorithms in this article : http://www.ise.ufl.edu/uryasev/portfoli ... t-risk.pdf .I've got some troubles implementing it. Does someone have a code for theses algorithms ?But this article is only optimization of the CVaR with respect to a given return. Could someone give me some papers with algorithms to avoid a large LP problem for the optimization of return with respect to a given CVaR ?Kind regards,Will

Hi Will,With 1000 scenarios all pivoting algs need to update a matrix of order 1000, so you need a storage of 1000^2, at least. I assume that you are using some simplex algorithm for dense problems. In fact your problem is sparse (as most MC methods are!), so you can write your algorithm for sparse matrices.I hope this solves your problem.

Thanks Borici for your answer !Do you know any way of dealing with sparse matrices in a linear optimization ? (maybe some algorithms or some papers ?)

http://directory.fsf.org/project/glpk/h ... ware/glpk/