Hi, what optimizer I can use (preferably in R) to solve the following portfolio optimization problem:
min(fTx)
st:
1. -a <= SUM x(i) <= b
2. -c <= x(i) <= d
3. e <= SUM |x(i)| <= f
4. SQRT (xT COV x) <= g
a,b,c,d,e,f,g - positive. f is a vector. x - weights. COV 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.
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Re: Portfolio optimization with factor tilting while constraining volatility
exactly! That is what I thought, though Mephist provides poor information about his aimsLagrange multiplier, barrier, penalty.
https://en.wikipedia.org/wiki/Lagrange_multiplier
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- Cuchulainn
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Re: Portfolio optimization with factor tilting while constraining volatility
A quick "constrained optimisation in R" throws up
https://cran.r-project.org/web/packages ... nloptr.pdf
etc.
https://cran.r-project.org/web/packages ... nloptr.pdf
etc.