\$TITLE simple MPEC unique solution LB matches integer var (MPEC08,SEQ=619) \$ontext extremely simple MPEC model with some useful features: a) it has a unique solution b) all matched vars are lower-bounded c) contains an integer var Contributor: Steve Dirkse, Sep 2013 \$offtext \$if not set TESTTOL \$set TESTTOL 1e-4 scalars tol / %TESTTOL% / c1 / -1.5 / c2 / -3 / ; positive variables x1, x2; integer variable y / lo 0, up 10 /; free variable z; equation f1, f2, o; f1 .. 2*x1 + x2 + y + c1 =N= 0; f2 .. x1 + 2*x2 + y + c2 =G= 0; o .. sqr(x1-2) + sqr(x2-2) + sqr(y-2) =E= z; model m / f1.x1, f2.x2, o /; scalars r1, r2; file log / '' /; * ----------------------------------------------------------------- solve m using rmpec 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; }; r1 = 2*x1.l + x2.l + y.l + c1; r2 = x1.l + 2*x2.l + y.l + c2; putclose log ' ' / '** RMPEC: y = ', y.L:6:2 / '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 / ' ' / ; abort\$(abs(x1.l-0 ) > tol) 'var x1.l should be 0' , x1.l; abort\$(abs(x2.l-0.8) > tol) 'var x2.l should be 0.8', x2.l; abort\$(abs( y.l-1.4) > tol) 'var y.l should be 1.4', y.l; abort\$(abs( z.l-5.8) > tol) 'var z.l should be 5.8', z.l; abort\$(abs(f1.l-0.7) > tol) 'equ f1.l should be 0.7', f1.l; abort\$(abs(f2.l-3.0) > tol) 'equ f2.l should be 3.0', f2.l; abort\$(abs( o.l-0 ) > tol) 'equ o.l should be 0' , o.l; * ----------------------------------------------------------------- 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.IntegerSolution% ] } ] 'Wrong status codes', m.solvestat, m.modelstat; }; r1 = 2*x1.l + x2.l + y.l + c1; r2 = x1.l + 2*x2.l + y.l + c2; putclose log ' ' / '** MPEC: y = ', y.L:6:2 / '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 / ' ' / ; abort\$(abs(x1.l-0 ) > tol) 'var x1.l should be 0' , x1.l; abort\$(abs(x2.l-1.0) > tol) 'var x2.l should be 1.0', x2.l; abort\$(abs( y.l-1.0) > tol) 'var y.l should be 1.0', y.l; abort\$(abs( z.l-6.0) > tol) 'var z.l should be 6.0', z.l; abort\$(abs(f1.l-0.5) > tol) 'equ f1.l should be 0.5', f1.l; abort\$(abs(f2.l-3.0) > tol) 'equ f2.l should be 3.0', f2.l; abort\$(abs( o.l-0 ) > tol) 'equ o.l should be 0' , o.l;