[R-SIG-Finance] mean-(scalar) portfolio optimization

[Brian G. Peterson]

The R function solve.QP is used by several authors to solve classic 
Markowitz mean-variance optimization using solve.QP and a covariance 
matrix.

Many other classes of portfolio optimization solve for the weighting 
vector w using a scalar measure of risk, such as VaR, Sortino, Omega, 
etc. 

Basically, this class of problems could be expressed as:

let w' be the desired portfolio weights
let R be a set of returns for various instruments

solve for a weighting vector w such that risk is minimized

w' = min(risk(R))

solve for a weighting vector w such that return is maximized over risk 
budget y

w'=max(mean(R)) such that risk(R)<.05

and other similar formulations.

solve.QP does not appear to be appropriate for these kinds of 
optimization.  The functions 'optim' and 'optimize' seem to return scalar 
values, solving only for a single minima or maxima, and not for the 
vector (although I may be misunderstanding them).

Does anyone have any pointers on how you might go about solving these 
kinds of optimization problems in R?  I apologize if this is a simple 
problem that I haven't been able to find a reference for online. I will 
happily post the optimizer code once it's working.

Thank you,

  - Brian