# qpec1.mod QQR2-MN-v-v
# Original AMPL coding by Sven Leyffer, University of Dundee
# A QPEC from H. Jiang and D. Ralph, Smooth SQP methods for mathematical
# programs with nonlinear complementarity constraints, University of
# Melbourne, December 1997.
# Number of variables: v
# Number of constraints: v
# ... parameters enlarge the problem
param n := 10; # number of controls (upper level vars)
param m := 20; # number of states (complementary vars)
set N := 1..n;
set M := 1..m; # NOTE: Assume m >= n
set NM := (n+1)..m;
# ... constants
param rr{N} := 1.0;
param ss{M} := 2.0;
# ... variables
var x{N};
var y{M} >= 0;
# ... problem statement
minimize f: sum{i in N}( (x[i] + rr[i])^2 ) + sum{j in M}( (y[j] + ss[j])^2 );
subject to
lin1{i in N}: 0 <= y[i] - x[i] complements y[i] >= 0;
lin2{i in NM}: 0 <= y[i] complements y[i] >= 0;
data;
let {i in N} x[i] := 1.0;
let {j in M} y[j] := 1.0;