qp6.gms : Standard QP Model - LCP formulation of QP4
Formulate the QP as an LCP, ie write down the first order
conditions of QP4 and solve.
Reference:
- Kalvelagen, E, Model Building with GAMS. forthcoming
Large Model of Type: MCP Includes: qpdata.inc
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$title Standard QP Model - QP4 expressed as MCP (QP6,SEQ=184)
$Ontext
Formulate the QP as an LCP, ie write down the first order
conditions of QP4 and solve.
Kalvelagen, E, Model Building with GAMS. forthcoming
de Wetering, A V, private communication.
$Offtext
$include qpdata.inc
set d(days) selected days
s(stocks) selected stocks
alias(s,t);
* select subset of stocks and periods
d(days) = ord(days) >1 and ord(days) < 31;
s(stocks) = ord(stocks) < 51;
parameter mean(stocks) mean of daily return
dev(stocks,days) deviations
totmean total mean return;
mean(s) = sum(d, return(s,d))/card(d);
dev(s,d) = return(s,d)-mean(s);
totmean = sum(s, mean(s))/(card(s));
variables x(stocks) investments
w(days) intermediate variables
;
positive variables x;
equations budget
retcon return constraint
wdef(days)
;
wdef(d).. w(d) =e= sum(s, x(s)*dev(s,d));
budget.. sum(s, x(s)) =e= 1.0;
retcon.. sum(s, mean(s)*x(s)) =g= totmean*1.25;
equations
d_x(stocks),
d_w(days);
variables
m_budget,
m_wdef(days);
positive variables
m_retcon;
m_wdef.fx(days)$(not d(days)) = 0;
d_x(s).. sum(d,m_wdef(d)*dev(s,d)) =g= m_retcon*mean(s) + m_budget;
d_w(d).. 2*w(d)/(card(d)-1) =e= m_wdef(d);
model qp6 /
d_x.x,
d_w.w,
retcon.m_retcon,
budget.m_budget,
wdef.m_wdef /;
solve qp6 using mcp;
parameter z;
z = sum(d, sqr(w.l(d)))/(card(d)-1);
display x.l,z;
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