void exprQuad::quadCuts (expression *w, OsiCuts &cs, const CouenneCutGenerator *cg){
#ifdef DEBUG
std::cout<<"Expression has "<< lcoeff_.size () <<" linear terms and "
<< nqterms_ <<" quadratic terms." << std::endl;
printf ("Q:");
for (sparseQ::iterator row = matrix_.begin (); row != matrix_.end (); ++row) {
int xind = row -> first -> Index ();
for (sparseQcol::iterator col = row -> second.begin (); col != row -> second.end (); ++col)
printf (" <%d,%d,%g>", xind, col -> first -> Index (), col -> second);
}
printf ("\nb:");
for (lincoeff::iterator el = lcoeff_.begin (); el != lcoeff_.end (); ++el)
//for (int i=0; i < nlterms_; i++)
printf (" <%d,%g>", el -> first -> Index (), el -> second);//index_ [i], coeff_ [i]);
if (c0_)
printf ("; <c0 = %g>", c0_);
printf ("\nBounds: var val lb ub eigval scaled\n");
int index = 0;
for (std::map <exprVar *, std::pair <CouNumber, CouNumber> >::iterator i = bounds_.begin ();
i != bounds_.end (); ++i, index++) {
printf ("%3d:\t", index);
i -> first -> print (); printf ("\t");
printf (" %8g [%8g, %8g]",
(*(i -> first)) (), i -> second.first, i -> second.second);
CouNumber
lb = cg -> Problem () -> Lb (i -> first -> Index ()),
ub = cg -> Problem () -> Ub (i -> first -> Index ());
if ((eigen_.size () > 0) &&
(fabs (ub-lb) > COUENNE_EPS))
printf (" --> %8g %8g",
eigen_.begin () -> first,
eigen_.begin () -> first / (ub-lb));
printf ("\n");
}
#endif
// Get on which side constraint is violated to get the good lambda
CouNumber
varVal = (*w) (),
exprVal = (*this) (),
lambda =
(eigen_.size () == 0) ? 0. :
(varVal < exprVal) ?
CoinMin (0., eigen_.begin () -> first) : // Use under-estimator
CoinMax (0., eigen_.rbegin () -> first), // Use over-estimator
convVal = 0.;
enum auxSign sign = cg -> Problem () -> Var (w -> Index ()) -> sign ();
// if this is a "semi"-auxiliary, check if necessary to separate
if ((sign == expression::AUX_GEQ && varVal > exprVal) ||
(sign == expression::AUX_LEQ && varVal < exprVal))
return;
const CouenneProblem& problem = *(cg -> Problem ());
const int numcols = problem.nVars ();
const double
*colsol = problem.X (), // current solution
*lower = problem.Lb (), // lower bound
*upper = problem.Ub (); // upper
// compute lower or upper convexification and check if it contains
// the current point
if (fabs (lambda) > COUENNE_EPS) {
convVal = exprVal;
// there is a convexification, check if out of current point
for (std::map <exprVar *, std::pair <CouNumber, CouNumber> >::iterator i = bounds_.begin ();
i != bounds_.end (); ++i) {
int ind = i -> first -> Index ();
CouNumber
xi = colsol [ind],
lb = lower [ind],
ub = upper [ind],
delta = ub-lb;
if (fabs (delta) > COUENNE_EPS)
convVal += lambda * (xi-lb) * (ub-xi) / (delta * delta);
}
if (varVal < exprVal) {if (convVal < varVal) return;}
else {if (convVal > varVal) return;}
}
#ifdef DEBUG
std::cout << "Point to cut: ";
for (int i = 0 ; i < numcols ; i++) std::cout << colsol [i] << ", ";
printf (" (w,f(x),c) = (%g,%g,%g) -- lambda = %g\n", (*w) (), exprVal, convVal, lambda);
#endif
// Initialize by copying $a$ into a dense vector and computing Q x^*
double
*Qxs = new double [numcols], // sparse coefficient vector, $Qx^*$
a0 = -c0_; // constant term
CoinFillN (Qxs, numcols, 0.);
// Compute 2 * Q x^*.
for (sparseQ::iterator row = matrix_.begin (); row != matrix_.end (); ++row) {
int qi = row -> first -> Index ();
for (sparseQcol::iterator col = row -> second.begin (); col != row -> second.end (); ++col) {
int qj = col -> first -> Index ();
CouNumber
qc = col -> second,
xi = colsol [qi],
xj = colsol [qj];
if (qi != qj) {
Qxs [qi] += qc * xj; // contribution of element $q_{ij}$ to (Qx)_i
Qxs [qj] += qc * xi; // $q_{ij}$ (Qx)_j
a0 += 2 * qc * xi * xj;
}
else {
/*
if (fabs (lambda) > COUENNE_EPS) {
CouNumber
lb = lower [qi],
ub = upper [qi],
delta = ub-lb;
if (fabs (delta) > COUENNE_EPS)
qc -= lambda / (delta*delta);
}
*/
// elements on the diagonal are not halved upon reading
a0 += qc * xi * xi;
Qxs [qi] += 2 * qc * xi;
}
}
}
#ifdef DEBUG
printf ("2Qx = ("); for (int i = 0; i < numcols; i++) printf ("%g ", Qxs [i]); printf (")\n");
#endif
// Add a to it.
for (lincoeff::iterator el = lcoeff_.begin (); el != lcoeff_.end (); ++el)
Qxs [el -> first -> Index ()] += el -> second; //coeff_ [i];
// multiply Qx^* by x^*^T again and store the result for the lower
// bound into constant term
/*
for (int i=0; i < numcols; i++){
a0 -= 0.5 * Qxs [i] * colsol [i];
// Qxs [i] *= 2;
}
*/
// And myself
Qxs [w -> Index ()] -= 1;
#ifdef DEBUG
printf ("2Qx = ("); for(int i = 0; i < numcols; i++) printf ("%g ", Qxs [i]); printf (")[%g]\n",a0);
#endif
//a0 -= exprVal;
if (fabs (lambda) > COUENNE_EPS) // Now the part which depends on lambda, if there is one
for (std::map <exprVar *, std::pair <CouNumber, CouNumber> >::iterator i = bounds_.begin ();
i != bounds_.end (); ++i) {
int ind = i -> first -> Index ();
CouNumber
xi = colsol [ind],
lb = lower [ind],
ub = upper [ind],
delta = ub-lb;
if (fabs (delta) > COUENNE_EPS) {
CouNumber normlambda = lambda / (delta*delta),
coeff = normlambda * (lb + ub - 2. * xi);
a0 += normlambda * (lb*ub - xi*xi);
//a0 += coeff * xi - normlambda * (xi - lb) * (ub - xi);
//a0 += normlambda * lb * ub;
Qxs [ind] += coeff;
//Qxs [ind] += normlambda * (lb + ub);
}// else coeff = 0.;
// a0 += lambda [k] * lower [ind] * upper [ind];
// a0 -= lambda [k] * colsol [ind] * colsol [ind];
//Qxs [ind] -= lambda [k] * (colsol [ind]) * 2;
}
// Count the number of non-zeroes
int nnz = 0;
for (int i=0; i < numcols ; i++)
if (fabs (Qxs [i]) > COUENNE_EPS)
nnz++;
#ifdef DEBUG
printf ("2Qx = (");for(int i=0;i<numcols;i++)printf("%g ",Qxs[i]);printf (")[%g], %d nz\n",a0,nnz);
#endif
// Pack the vector into a CoinPackedVector and generate the cut.
CoinPackedVector a (false);
a.reserve (nnz);
#ifdef DEBUG
CouNumber lhs = 0, lhsc = 0,
*optimum = cg -> Problem () -> bestSol (),
*current = cg -> Problem () -> X ();
#endif
for (int i=0; i < numcols; i++)
if (fabs (Qxs [i]) > 1.0e-21) { // why 1.0e-21? Look at CoinPackedMatrix.cpp:2188
// compute violation
#ifdef DEBUG
if (optimum) {
printf ("%+g * %g ", Qxs [i], optimum [i]);
lhs += Qxs [i] * optimum [i];
}
lhsc += Qxs [i] * current [i];
#endif
a.insert (i, Qxs [i]);
}
OsiRowCut cut;
cut.setRow (a);
delete [] Qxs;
if (varVal < exprVal) { //(lambda == dCoeffLo_) {
cut.setUb (a0);
#ifdef DEBUG
if (optimum && (lhs - a0 > COUENNE_EPS)) {
printf ("cut violates optimal solution: %g > %g\n", lhs, a0);
cut.print ();
}
if (lhsc < a0 + COUENNE_EPS){
printf ("cut (+) is not cutting: ");
cut.print ();
}
#endif
// cut.setLb(-COUENNE_INFINITY);
}
else {
cut.setLb (a0);
#ifdef DEBUG
if (optimum && (lhs - a0 < -COUENNE_EPS)) {
printf ("cut violates optimal solution: %g < %g\n", lhs, a0);
cut.print ();
}
if (lhsc > a0 - COUENNE_EPS){
printf ("cut (-) is not cutting: ");
cut.print ();
}
#endif
// cut.setUb(COUENNE_INFINITY);
}
cs.insert (cut);
}
