qp2.gms : Standard QP Model - symmetry exploitations
This version better exploits the symmetry of a quadratic form.
Additional information can be found at:
http://www.gams.com/modlib/adddocs/qp2doc.htm
Reference:
- Kalvelagen, E, Model Building with GAMS. forthcoming
Small Model of Type: NLP Includes: qpdata.inc
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$title Standard QP Model - symmetry exploitations (QP2,SEQ=172)
$Ontext
This version better exploits the symmetry of a quadratic form.
Additional information can be found at:
http://www.gams.com/modlib/adddocs/qp2doc.htm
Kalvelagen, E, Model Building with GAMS. forthcoming
de Wetering, A V, private communication.
$Offtext
$include qpdata.inc
set d(days) selected days
s(stocks) selected stocks
alias(s,t);
* select subset of stocks and periods
d(days) = ord(days) >1 and ord(days) < 31;
s(stocks) = ord(stocks) < 51;
parameter mean(stocks) mean of daily return
dev(stocks,days) deviations
covar(stocks,sstocks) covariance matrix of returns (upper)
totmean total mean return;
mean(s) = sum(d, return(s,d))/card(d);
dev(s,d) = return(s,d)-mean(s);
* calculate covariance
* to save memory and time we only compute the uppertriangular
* part as the covariance matrix is symmetric
covar(upper(s,t)) = 2*sum(d, dev(s,d)*dev(t,d))/(card(d)-1);
covar(s,s) = covar(s,s)/2;
totmean = sum(s, mean(s))/(card(s));
variables z objective variable
x(stocks) investments;
positive variables x;
equations obj objective
budget
retcon return constraint
;
obj.. z =e= sum((s,t), x(s)*covar(s,t)*x(t));
budget.. sum(s, x(s)) =e= 1.0;
retcon.. sum(s, mean(s)*x(s)) =g= totmean*1.25;
model qp2 /all/;
* Some solvers need more memory
qp2.workfactor = 6;
solve qp2 using nlp minizing z;
display x.l;
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