4 messages · Gottfried Gruber, Arne Henningsen, Jim McLoughlin
hi, i want to execute the following opimization problem: max r*w s.t.: w*z=1 # sum of w is 1 r, w are [nx1] vectors, z is a [nx1] vector consisting of 1 so far so good, works fine with lp the problem arises with the additional restriction w' * V * w where V is a [nxn] matrix how can i include this restriction since w arises twice? thanks, gg
--------------------------------------------------- Gottfried Gruber mailto:gottfried.gruber at terminal.at www: http://gogo.sehrsupa.net
Hi Gottfried, w' * V * w is not a restriction, because there is no equal sign. Do you mean w' * V * w = 1? Arne
hi, i want to execute the following opimization problem: max r*w s.t.: w*z=1 # sum of w is 1 r, w are [nx1] vectors, z is a [nx1] vector consisting of 1 so far so good, works fine with lp the problem arises with the additional restriction w' * V * w where V is a [nxn] matrix how can i include this restriction since w arises twice? thanks, gg
Arne Henningsen Department of Agricultural Economics University of Kiel Olshausenstr. 40 D-24098 Kiel (Germany) Tel: +49-431-880 4445 Fax: +49-431-880 1397 ahenningsen at agric-econ.uni-kiel.de http://www.uni-kiel.de/agrarpol/ahenningsen/
Hi Arne, i'm sorry - the additional restriction is w' * V * w <= j where j is a [1x1] matrix. i don't know how to incorporate this restriction in the lp-object. would be grateful on any response, thanks, gg
Hi Gottfried, w' * V * w is not a restriction, because there is no equal sign. Do you mean w' * V * w = 1? Arne On Sunday 01 May 2005 19:21, Gottfried Gruber wrote:
hi, i want to execute the following opimization problem: max r*w s.t.: w*z=1 # sum of w is 1 r, w are [nx1] vectors, z is a [nx1] vector consisting of 1 so far so good, works fine with lp the problem arises with the additional restriction w' * V * w where V is a [nxn] matrix how can i include this restriction since w arises twice? thanks, gg
--------------------------------------------------- Gottfried Gruber mailto:gottfried.gruber at terminal.at www: http://gogo.sehrsupa.net
The form of the problem looks like you are trying to do a mean-variance portfolio optimization. If that is the case, you should not be dealing with variance as a restriction, but as part of the objective function: max (r'*w - rho*w'*V*w) s.t. sum(w) == 1 where rho is a risk aversion parameter. You can solve this as a quadratic programming problem using either 1) solve.QP from the quadprog package; 2) portfolio.optim in package tseries see http://tolstoy.newcastle.edu.au/R/help/05/01/10505.html for details on how to use the two.
On Sunday 01 May 2005 19:21, Gottfried Gruber wrote:
hi, i want to execute the following opimization problem: max r*w s.t.: w*z=1 # sum of w is 1 r, w are [nx1] vectors, z is a [nx1] vector consisting of 1 so far so good, works fine with lp the problem arises with the additional restriction w' * V * w where V is a [nxn] matrix how can i include this restriction since w arises twice?