\$TITLE simple MPEC unique solution doubly-bounded matches (MPEC07,SEQ=618) \$ontext extremely simple MPEC model with some useful features: a) it has a unique solution b) all matched vars are doubly-bounded Contributor: Steve Dirkse, Sep 2013 \$offtext \$if not set TESTTOL \$set TESTTOL 1e-4 scalars tol / %TESTTOL% / c1 / -4 / c2 / 8 / c3 / 8 / ; free variables x1 / lo -1, up 1 / x2 / lo 1, up 3 / x3 / lo -100, up 100 / y / up 0 / ; free variable z; equation f1, f2, f3, o; f1 .. 3*x1 + x2 + y + c1 =N= 0; f2 .. x1 + 3*x2 + x3 + y + c2 =G= 0; f3 .. x2 + 3*x3 + y + c3 =N= 0; o .. sqr(x1-5) + sqr(x2-2) + sqr(x3-2) + sqr(y) =E= z; model m / f1.x1, f2.x2, f3.x3, o /; solve m using mpec min z; if {(m.solvestat = %solvestat.CapabilityProblems%), abort\$[m.modelstat <> %modelstat.NoSolutionReturned%] 'Wrong status codes', m.solvestat, m.modelstat; abort.noerror 'no solution, no point in checking further'; else abort\$[not((m.solvestat = %solvestat.NormalCompletion%) and (m.modelstat = %modelstat.Optimal% or m.modelstat = %modelstat.LocallyOptimal% or m.modelstat = %modelstat.FeasibleSolution%))] 'Wrong status codes', m.solvestat, m.modelstat; }; scalars r1, r2, r3; r1 = 3*x1.l + x2.l + y.l + c1; r2 = x1.l + 3*x2.l + x3.l + y.l + c2; r3 = x2.l + 3*x3.l + y.l + c3; file log / '' /; putclose log ' ' / 'F1 := ', r1:6:2, ' perp x1 ', x1.lo:8:2, ' <= ', x1.L:6:2 ' <= ', x1.up:6:2 / 'F2 := ', r2:6:2, ' perp x2 ', x2.lo:8:2, ' <= ', x2.L:6:2 ' <= ', x2.up:6:2 / 'F3 := ', r3:6:2, ' perp x3 ', x3.lo:8:2, ' <= ', x3.L:6:2 ' <= ', x3.up:6:2 / ' y = ', y.L:6:2 / ' ' / ; abort\$(abs(x1.l-1.0) > tol) 'var x1.l should be 1.0', x1.l; abort\$(abs(x2.l-1.0) > tol) 'var x2.l should be 1.0', x2.l; abort\$(abs(x3.l+2.5) > tol) 'var x3.l should be -2.5', x3.l; abort\$(abs( y.l+1.5) > tol) 'var y.l should be -1.5', y.l; abort\$(abs( z.l-39.5)> tol) 'var z.l should be 39.5', z.l; abort\$(abs(f1.l+1.5) > tol) 'equ f1.l should be -1.5', f1.l; abort\$(abs(f2.l-0.0) > tol) 'equ f2.l should be 0.0', f2.l; abort\$(abs(f3.l-0.0) > tol) 'equ f3.l should be 0.0', f3.l; abort\$(abs( o.l-0 ) > tol) 'equ o.l should be 0' , o.l;