Hi,

You can try a projected gradient approach, which is implemented in the spg() 
function in the "BB" package. You have to provide a projection function which 
will take an infeasible matrix as input and will give a feasible (i.e. 
positive-definite) matrix as output. This kind of matrix projection is quite 
easy to do, and in fact, there are functions in R to do this (e.g., see 
posdefify() function in "sfsmisc" package).


There is a recent review article on spectral projected gradient algorithm in J 
Statistical Software.

http://www.jstatsoft.org/v60/i03


Hope this is helpful,

Ravi

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