what optimizer I can use in R to solve the following portfolio optimization problem:
$min(f^Tx)$
st:
1. $ -a \le \sum_{i=1} ^{n} x(i) \le b$
2. $ -c \le x(i) \le d$
3. $ e \le \sum _{i=1} ^n |x(i)| \le f$
4. $\sqrt{x^t\Sigma x} \le g$
a,b,c,d,e,f,g - positive. f is a vector. x - weights. $\Sigma$ var-covar matrix estimated from historical data. The problem without constrain 4 can be solved with linear solver ( with some tricks for condition 3). Condition 4 makes constrain non-linear, but quadratic. Any suggestion would be helpful. Thanks.