qp1.gms : Standard QP Model
The first in a series of variations on the standard
QP formulation. The subsequent models exploit data
and problem structures to arrive at formulations that
have sensational computational advantages. Additional
information can be found at:
http://www.gams.com/modlib/adddocs/qp1doc.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 (QP1,SEQ=171)
$Ontext
The first in a series of variations on the standard
QP formulation. The subsequent models exploit data
and problem structures to arrive at formulations that
have sensational computational advantages. Additional
information can be found at:
http://www.gams.com/modlib/adddocs/qp1doc.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)) = sum(d, dev(s,d)*dev(t,d))/(card(d)-1);
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(upper(s,t), x(s)*covar(s,t)*x(t)) +
sum(lower(s,t), x(s)*covar(t,s)*x(t));
budget.. sum(s, x(s)) =e= 1.0;
retcon.. sum(s, mean(s)*x(s)) =g= totmean*1.25;
model qp1 /all/;
* Some solvers need more memory
qp1.workfactor = 10;
solve qp1 using nlp minizing z;
display x.l;
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