[R] linear constraint optim with bounds/reparametrization
kahra at mpsgr.it
Thu Aug 12 17:56:05 CEST 2004
>From Spencer Graves:
>However, for an equality constraint, I've had good luck by with an objective function that adds something like the
>following to my objective function: constraintViolationPenalty*(A%*%theta-c)^2, where "constraintViolationPenalty" is
>passed via "..." in a call to optim.
I applied Spencer's suggestion to a set of eight different constrained portfolio optimization problems. It seems to give a usable practice to solve the portfolio problem, when the QP optimizer is not applicable. After all, practical portfolio management is more an art than a science.
>I may first run optim with a modest value for constraintViolationPenalty then restart it with the output of the
>initial run as starting values and with a larger value for constraintViolationPenalty.
I wrote a loop that starts with a small value for the penalty and stops when the change of the function value, when increasing the penalty, is less than epsilon. I found that epsilon = 1e-06 provides a reasonable accuracy with respect to computational time.
Spencer, many thanks for your suggestion.
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