// NOTE: CPLEX does not provide a function to directly get the dual
// multipliers for second order cone constraint.
// Example QCPDual.cs illustrates how the dual multipliers for a
// quadratic constraint can be computed from that constraint's
// slack.
// However, for SOCP we can do something simpler: we can read those
// multipliers directly from the dual slacks for the
// cone head variables. For a second order cone constraint
// x[1] >= |(x[2], ..., x[n])|
// the dual multiplier is the dual slack value for x[1].
/// <summary>
/// Compute dual multipliers for second order cone constraints.
/// Returns a dictionary with a dual multiplier for each second order cone
/// constraint.
/// </summary>
/// <remarks>
/// <c>cplex</c> is the Cplex instance with the optimal solution.
/// <c>vars</c> is a collection with <em>all</em> variables in the model.
/// <c>rngs</c> is a collection with <em>all</em> constraints in the
/// model.
/// <c>dslack</c> is a dictionary in which the function will store the full
/// dual slack, provided the argument is not <c>null</c>.
/// </remarks>
private static IDictionary <IRange, System.Double> Getsocpconstrmultipliers(Cplex cplex, ICollection <INumVar> vars, ICollection <IRange> rngs, IDictionary <INumVar, System.Double> dslack)
{
// Compute full dual slack.
IDictionary <INumVar, System.Double> dense = new SortedDictionary <INumVar, System.Double>(NumVarComparator);
foreach (INumVar v in vars)
{
dense[v] = cplex.GetReducedCost(v);
}
foreach (IRange r in rngs)
{
INumExpr e = r.Expr;
if ((e is IQuadNumExpr) && ((IQuadNumExpr)e).GetQuadEnumerator().MoveNext())
{
// Quadratic constraint: pick up dual slack vector
for (ILinearNumExprEnumerator it = cplex.GetQCDSlack(r).GetLinearEnumerator(); it.MoveNext(); /* nothing */)
{
dense[it.NumVar] = dense[it.NumVar] + it.Value;
}
}
}
// Find the cone head variables and pick up the dual slacks for them.
IDictionary <IRange, System.Double> socppi = new SortedDictionary <IRange, System.Double>(RangeComparator);
foreach (IRange r in rngs)
{
INumExpr e = r.Expr;
if ((e is IQuadNumExpr) && ((IQuadNumExpr)e).GetQuadEnumerator().MoveNext())
{
// Quadratic constraint: pick up dual slack vector
for (IQuadNumExprEnumerator it = ((IQuadNumExpr)e).GetQuadEnumerator(); it.MoveNext(); /* nothing */)
{
if (it.Value < 0)
{
socppi[r] = dense[it.NumVar1];
break;
}
}
}
}
// Fill in the dense slack if the user asked for it.
if (dslack != null)
{
dslack.Clear();
foreach (INumVar v in dense.Keys)
{
dslack[v] = dense[v];
}
}
return(socppi);
}
// Print out the objective function.
// Note that the quadratic expression in the objective
// is normalized: i.E., for all i != j, terms
// c(i,j)*x[i]*x[j] + c(j,i)*x[j]*x[i] is normalized as
// (c(i,j) + c(j,i)) * x[i]*x[j], or
// (c(i,j) + c(j,i)) * x[j]*x[i].
internal static void PrintObjective(IObjective obj)
{
System.Console.WriteLine("obj: " + obj);
// Count the number of linear terms
// in the objective function.
int nlinterms = 0;
ILinearNumExprEnumerator len = ((ILQNumExpr)obj.Expr).GetLinearEnumerator();
while (len.MoveNext())
{
++nlinterms;
}
// Count the number of quadratic terms
// in the objective function.
int nquadterms = 0;
int nquaddiag = 0;
IQuadNumExprEnumerator qen = ((ILQNumExpr)obj.Expr).GetQuadEnumerator();
while (qen.MoveNext())
{
++nquadterms;
INumVar var1 = qen.GetNumVar1();
INumVar var2 = qen.GetNumVar2();
if (var1.Equals(var2))
{
++nquaddiag;
}
}
System.Console.WriteLine("number of linear terms in the objective : " + nlinterms);
System.Console.WriteLine("number of quadratic terms in the objective : " + nquadterms);
System.Console.WriteLine("number of diagonal quadratic terms in the objective : " + nquaddiag);
System.Console.WriteLine();
}
/* Test KKT conditions on the solution.
* The function returns true if the tested KKT conditions are satisfied
* and false otherwise.
*/
private static bool Checkkkt(Cplex cplex,
IObjective obj,
ICollection <INumVar> vars,
ICollection <IRange> rngs,
IDictionary <INumVar, IRange> cone,
double tol)
{
System.IO.TextWriter error = cplex.Output();
System.IO.TextWriter output = cplex.Output();
IDictionary <INumVar, System.Double> dslack = new SortedDictionary <INumVar, System.Double>(NumVarComparator);
IDictionary <INumVar, System.Double> x = new SortedDictionary <INumVar, System.Double>(NumVarComparator);
IDictionary <IRange, System.Double> pi = new SortedDictionary <IRange, System.Double>(RangeComparator);
IDictionary <IRange, System.Double> slack = new SortedDictionary <IRange, System.Double>(RangeComparator);
// Read primal and dual solution information.
foreach (INumVar v in vars)
{
x[v] = cplex.GetValue(v);
}
pi = Getsocpconstrmultipliers(cplex, vars, rngs, dslack);
foreach (IRange r in rngs)
{
slack[r] = cplex.GetSlack(r);
INumExpr e = r.Expr;
if (!(e is IQuadNumExpr) || !((IQuadNumExpr)e).GetQuadEnumerator().MoveNext())
{
// Linear constraint: get the dual value
pi[r] = cplex.GetDual(r);
}
}
// Print out the data we just fetched.
output.Write("x = [");
foreach (INumVar v in vars)
{
output.Write(" {0,7:0.000}", x[v]);
}
output.WriteLine(" ]");
output.Write("dslack = [");
foreach (INumVar v in vars)
{
output.Write(" {0,7:0.000}", dslack[v]);
}
output.WriteLine(" ]");
output.Write("pi = [");
foreach (IRange r in rngs)
{
output.Write(" {0,7:0.000}", pi[r]);
}
output.WriteLine(" ]");
output.Write("slack = [");
foreach (IRange r in rngs)
{
output.Write(" {0,7:0.000}", slack[r]);
}
output.WriteLine(" ]");
// Test primal feasibility.
// This example illustrates the use of dual vectors returned by CPLEX
// to verify dual feasibility, so we do not test primal feasibility
// here.
// Test dual feasibility.
// We must have
// - for all <= constraints the respective pi value is non-negative,
// - for all >= constraints the respective pi value is non-positive,
// - the dslack value for all non-cone variables must be non-negative.
// Note that we do not support ranged constraints here.
foreach (INumVar v in vars)
{
if (cone[v] == NOT_IN_CONE && dslack[v] < -tol)
{
error.WriteLine("Dual multiplier for " + v + " is not feasible: " + dslack[v]);
return(false);
}
}
foreach (IRange r in rngs)
{
if (System.Math.Abs(r.LB - r.UB) <= tol)
{
// Nothing to check for equality constraints.
}
else if (r.LB > -System.Double.MaxValue && pi[r] > tol)
{
error.WriteLine("Dual multiplier " + pi[r] + " for >= constraint");
error.WriteLine(" " + r);
error.WriteLine("not feasible.");
return(false);
}
else if (r.UB < System.Double.MaxValue && pi[r] < -tol)
{
error.WriteLine("Dual multiplier " + pi[r] + " for <= constraint");
error.WriteLine(" " + r);
error.WriteLine("not feasible.");
return(false);
}
}
// Test complementary slackness.
// For each constraint either the constraint must have zero slack or
// the dual multiplier for the constraint must be 0. We must also
// consider the special case in which a variable is not explicitly
// contained in a second order cone constraint.
foreach (INumVar v in vars)
{
if (cone[v] == NOT_IN_CONE)
{
if (System.Math.Abs(x[v]) > tol && dslack[v] > tol)
{
error.WriteLine("Invalid complementary slackness for " + v + ":");
error.WriteLine(" " + x[v] + " and " + dslack[v]);
return(false);
}
}
}
foreach (IRange r in rngs)
{
if (System.Math.Abs(slack[r]) > tol && System.Math.Abs(pi[r]) > tol)
{
error.WriteLine("Invalid complementary slackness for");
error.WriteLine(" " + r);
error.WriteLine(" " + slack[r] + " and " + pi[r]);
return(false);
}
}
// Test stationarity.
// We must have
// c - g[i]'(X)*pi[i] = 0
// where c is the objective function, g[i] is the i-th constraint of the
// problem, g[i]'(x) is the derivate of g[i] with respect to x and X is the
// optimal solution.
// We need to distinguish the following cases:
// - linear constraints g(x) = ax - b. The derivative of such a
// constraint is g'(x) = a.
// - second order constraints g(x[1],...,x[n]) = -x[1] + |(x[2],...,x[n])|
// the derivative of such a constraint is
// g'(x) = (-1, x[2]/|(x[2],...,x[n])|, ..., x[n]/|(x[2],...,x[n])|
// (here |.| denotes the Euclidean norm).
// - bound constraints g(x) = -x for variables that are not explicitly
// contained in any second order cone constraint. The derivative for
// such a constraint is g'(x) = -1.
// Note that it may happen that the derivative of a second order cone
// constraint is not defined at the optimal solution X (this happens if
// X=0). In this case we just skip the stationarity test.
IDictionary <INumVar, System.Double> sum = new SortedDictionary <INumVar, System.Double>(NumVarComparator);
foreach (INumVar v in vars)
{
sum[v] = 0.0;
}
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)cplex.GetObjective().Expr).GetLinearEnumerator(); it.MoveNext(); /* nothing */)
{
sum[it.NumVar] = it.Value;
}
foreach (INumVar v in vars)
{
if (cone[v] == NOT_IN_CONE)
{
sum[v] = sum[v] - dslack[v];
}
}
foreach (IRange r in rngs)
{
INumExpr e = r.Expr;
if ((e is IQuadNumExpr) && ((IQuadNumExpr)e).GetQuadEnumerator().MoveNext())
{
double norm = 0.0;
for (IQuadNumExprEnumerator q = ((IQuadNumExpr)e).GetQuadEnumerator(); q.MoveNext(); /* nothing */)
{
if (q.Value > 0)
{
norm += x[q.NumVar1] * x[q.NumVar1];
}
}
norm = System.Math.Sqrt(norm);
if (System.Math.Abs(norm) <= tol)
{
cplex.Warning().WriteLine("Cannot check stationarity at non-differentiable point");
return(true);
}
for (IQuadNumExprEnumerator q = ((IQuadNumExpr)e).GetQuadEnumerator(); q.MoveNext(); /* nothing */)
{
INumVar v = q.NumVar1;
if (q.Value < 0)
{
sum[v] = sum[v] - pi[r];
}
else if (q.Value > 0)
{
sum[v] = sum[v] + pi[r] * x[v] / norm;
}
}
}
else if (e is ILinearNumExpr)
{
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)e).GetLinearEnumerator(); it.MoveNext(); /* nothing */)
{
INumVar v = it.NumVar;
sum[v] = sum[v] - pi[r] * it.Value;
}
}
}
// Now test that all elements in sum[] are 0.
foreach (INumVar v in vars)
{
if (System.Math.Abs(sum[v]) > tol)
{
error.WriteLine("Invalid stationarity " + sum[v] + " for " + v);
return(false);
}
}
return(true);
}
/* ***************************************************************** *
* *
* C A L C U L A T E D U A L S F O R Q U A D S *
* *
* CPLEX does not give us the dual multipliers for quadratic *
* constraints directly. This is because they may not be properly *
* defined at the cone top and deciding whether we are at the cone *
* top or not involves (problem specific) tolerance issues. CPLEX *
* instead gives us all the values we need in order to compute the *
* dual multipliers if we are not at the cone top. *
* *
* ***************************************************************** */
/// <summary>
/// Calculate dual multipliers for quadratic constraints from dual
/// slack vectors and optimal solutions.
/// The dual multiplier is essentially the dual slack divided
/// by the derivative evaluated at the optimal solution. If the optimal
/// solution is 0 then the derivative at this point is not defined (we are
/// at the cone top) and we cannot compute a dual multiplier.
/// </summary>
/// <remarks>
/// <c>cplex</c> is the Cplex instance that holds the optimal
/// solution.
/// <c>xval</c> is the optimal solution vector.
/// <c>tol</c> is the tolerance used to decide whether we are at
/// the cone
/// <c>x</c> is the array of variables in the model.
/// <c>qs</c> is the array of quadratic constraints for which duals
/// shall be calculated.
/// </remarks>
private static double[] getqconstrmultipliers(Cplex cplex, double[] xval, double tol, INumVar[] x, IRange[] qs)
{
double[] qpi = new double[qs.Length];
// Store solution in map so that we can look up by variable.
IDictionary <INumVar, System.Double> sol = new Dictionary <INumVar, System.Double>();
for (int j = 0; j < x.Length; ++j)
{
sol.Add(x[j], xval[j]);
}
for (int i = 0; i < qs.Length; ++i)
{
IDictionary <INumVar, System.Double> dslack = new Dictionary <INumVar, System.Double>();
for (ILinearNumExprEnumerator it = cplex.GetQCDSlack(qs[i]).GetLinearEnumerator(); it.MoveNext(); /* nothing */)
{
dslack[it.NumVar] = it.Value;
}
IDictionary <INumVar, System.Double> grad = new Dictionary <INumVar, System.Double>();
bool conetop = true;
for (IQuadNumExprEnumerator it = ((ILQNumExpr)qs[i].Expr).GetQuadEnumerator();
it.MoveNext(); /* nothing */)
{
INumVar x1 = it.NumVar1;
INumVar x2 = it.NumVar2;
if (sol[x1] > tol || sol[x2] > tol)
{
conetop = false;
}
System.Double old;
if (!grad.TryGetValue(x1, out old))
{
old = 0.0;
}
grad[x1] = old + sol[x2] * it.Value;
if (!grad.TryGetValue(x2, out old))
{
old = 0.0;
}
grad[x2] = old + sol[x1] * it.Value;
}
if (conetop)
{
throw new System.SystemException("Cannot compute dual multiplier at cone top!");
}
// Compute qpi[i] as slack/gradient.
// We may have several indices to choose from and use the one
// with largest absolute value in the denominator.
bool ok = false;
double maxabs = -1.0;
foreach (INumVar v in x)
{
System.Double g;
if (grad.TryGetValue(v, out g))
{
if (System.Math.Abs(g) > tol)
{
if (System.Math.Abs(g) > maxabs)
{
System.Double d;
qpi[i] = (dslack.TryGetValue(v, out d) ? d : 0.0) / g;
maxabs = System.Math.Abs(g);
}
ok = true;
}
}
}
if (!ok)
{
// Dual slack is all 0. qpi[i] can be anything, just set to 0.
qpi[i] = 0;
}
}
return(qpi);
}
/// <summary>
/// The example's main function.
/// </summary>
public static void Main(string[] args)
{
int retval = 0;
Cplex cplex = null;
try
{
cplex = new Cplex();
/* ***************************************************************** *
* *
* S E T U P P R O B L E M *
* *
* We create the following problem: *
* Minimize *
* obj: 3x1 - x2 + 3x3 + 2x4 + x5 + 2x6 + 4x7 *
* Subject To *
* c1: x1 + x2 = 4 *
* c2: x1 + x3 >= 3 *
* c3: x6 + x7 <= 5 *
* c4: -x1 + x7 >= -2 *
* q1: [ -x1^2 + x2^2 ] <= 0 *
* q2: [ 4.25x3^2 -2x3*x4 + 4.25x4^2 - 2x4*x5 + 4x5^2 ] + 2 x1 <= 9.0
* q3: [ x6^2 - x7^2 ] >= 4 *
* Bounds *
* 0 <= x1 <= 3 *
* x2 Free *
* 0 <= x3 <= 0.5 *
* x4 Free *
* x5 Free *
* x7 Free *
* End *
* *
* ***************************************************************** */
INumVar[] x = new INumVar[7];
x[0] = cplex.NumVar(0, 3, "x1");
x[1] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x2");
x[2] = cplex.NumVar(0, 0.5, "x3");
x[3] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x4");
x[4] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x5");
x[5] = cplex.NumVar(0, System.Double.PositiveInfinity, "x6");
x[6] = cplex.NumVar(System.Double.NegativeInfinity, System.Double.PositiveInfinity, "x7");
IRange[] linear = new IRange[4];
linear[0] = cplex.AddEq(cplex.Sum(x[0], x[1]), 4.0, "c1");
linear[1] = cplex.AddGe(cplex.Sum(x[0], x[2]), 3.0, "c2");
linear[2] = cplex.AddLe(cplex.Sum(x[5], x[6]), 5.0, "c3");
linear[3] = cplex.AddGe(cplex.Diff(x[6], x[0]), -2.0, "c4");
IRange[] quad = new IRange[3];
quad[0] = cplex.AddLe(cplex.Sum(cplex.Prod(-1, x[0], x[0]),
cplex.Prod(x[1], x[1])), 0.0, "q1");
quad[1] = cplex.AddLe(cplex.Sum(cplex.Prod(4.25, x[2], x[2]),
cplex.Prod(-2, x[2], x[3]),
cplex.Prod(4.25, x[3], x[3]),
cplex.Prod(-2, x[3], x[4]),
cplex.Prod(4, x[4], x[4]),
cplex.Prod(2, x[0])), 9.0, "q2");
quad[2] = cplex.AddGe(cplex.Sum(cplex.Prod(x[5], x[5]),
cplex.Prod(-1, x[6], x[6])), 4.0, "q3");
cplex.AddMinimize(cplex.Sum(cplex.Prod(3.0, x[0]),
cplex.Prod(-1.0, x[1]),
cplex.Prod(3.0, x[2]),
cplex.Prod(2.0, x[3]),
cplex.Prod(1.0, x[4]),
cplex.Prod(2.0, x[5]),
cplex.Prod(4.0, x[6])), "obj");
/* ***************************************************************** *
* *
* O P T I M I Z E P R O B L E M *
* *
* ***************************************************************** */
cplex.SetParam(Cplex.Param.Barrier.QCPConvergeTol, 1e-10);
cplex.Solve();
/* ***************************************************************** *
* *
* Q U E R Y S O L U T I O N *
* *
* ***************************************************************** */
double[] xval = cplex.GetValues(x);
double[] slack = cplex.GetSlacks(linear);
double[] qslack = cplex.GetSlacks(quad);
double[] cpi = cplex.GetReducedCosts(x);
double[] rpi = cplex.GetDuals(linear);
double[] qpi = getqconstrmultipliers(cplex, xval, ZEROTOL, x, quad);
// Also store solution in a dictionary so that we can look up
// values by variable and not only by index.
IDictionary <INumVar, System.Double> xmap = new Dictionary <INumVar, System.Double>();
for (int j = 0; j < x.Length; ++j)
{
xmap.Add(x[j], xval[j]);
}
/* ***************************************************************** *
* *
* C H E C K K K T C O N D I T I O N S *
* *
* Here we verify that the optimal solution computed by CPLEX *
* (and the qpi[] values computed above) satisfy the KKT *
* conditions. *
* *
* ***************************************************************** */
// Primal feasibility: This example is about duals so we skip this test.
// Dual feasibility: We must verify
// - for <= constraints (linear or quadratic) the dual
// multiplier is non-positive.
// - for >= constraints (linear or quadratic) the dual
// multiplier is non-negative.
for (int i = 0; i < linear.Length; ++i)
{
if (linear[i].LB <= System.Double.NegativeInfinity)
{
// <= constraint
if (rpi[i] > ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for row " + linear[i]
+ ": " + rpi[i]);
}
}
else if (linear[i].UB >= System.Double.PositiveInfinity)
{
// >= constraint
if (rpi[i] < -ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for row " + linear[i]
+ ": " + rpi[i]);
}
}
else
{
// nothing to do for equality constraints
}
}
for (int i = 0; i < quad.Length; ++i)
{
if (quad[i].LB <= System.Double.NegativeInfinity)
{
// <= constraint
if (qpi[i] > ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for quad " + quad[i]
+ ": " + qpi[i]);
}
}
else if (quad[i].UB >= System.Double.PositiveInfinity)
{
// >= constraint
if (qpi[i] < -ZEROTOL)
{
throw new System.SystemException("Dual feasibility test failed for quad " + quad[i]
+ ": " + qpi[i]);
}
}
else
{
// nothing to do for equality constraints
}
}
// Complementary slackness.
// For any constraint the product of primal slack and dual multiplier
// must be 0.
for (int i = 0; i < linear.Length; ++i)
{
if (System.Math.Abs(linear[i].UB - linear[i].LB) > ZEROTOL &&
System.Math.Abs(slack[i] * rpi[i]) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for row " + linear[i]
+ ": " + System.Math.Abs(slack[i] * rpi[i]));
}
}
for (int i = 0; i < quad.Length; ++i)
{
if (System.Math.Abs(quad[i].UB - quad[i].LB) > ZEROTOL &&
System.Math.Abs(qslack[i] * qpi[i]) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for quad " + quad[i]
+ ": " + System.Math.Abs(qslack[i] * qpi[i]));
}
}
for (int j = 0; j < x.Length; ++j)
{
if (x[j].UB < System.Double.PositiveInfinity)
{
double slk = x[j].UB - xval[j];
double dual = cpi[j] < -ZEROTOL ? cpi[j] : 0.0;
if (System.Math.Abs(slk * dual) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for column " + x[j]
+ ": " + System.Math.Abs(slk * dual));
}
}
if (x[j].LB > System.Double.NegativeInfinity)
{
double slk = xval[j] - x[j].LB;
double dual = cpi[j] > ZEROTOL ? cpi[j] : 0.0;
if (System.Math.Abs(slk * dual) > ZEROTOL)
{
throw new System.SystemException("Complementary slackness test failed for column " + x[j]
+ ": " + System.Math.Abs(slk * dual));
}
}
}
// Stationarity.
// The difference between objective function and gradient at optimal
// solution multiplied by dual multipliers must be 0, i.E., for the
// optimal solution x
// 0 == c
// - sum(r in rows) r'(x)*rpi[r]
// - sum(q in quads) q'(x)*qpi[q]
// - sum(c in cols) b'(x)*cpi[c]
// where r' and q' are the derivatives of a row or quadratic constraint,
// x is the optimal solution and rpi[r] and qpi[q] are the dual
// multipliers for row r and quadratic constraint q.
// b' is the derivative of a bound constraint and cpi[c] the dual bound
// multiplier for column c.
IDictionary <INumVar, System.Double> kktsum = new Dictionary <INumVar, System.Double>();
for (int j = 0; j < x.Length; ++j)
{
kktsum.Add(x[j], 0.0);
}
// Objective function.
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)cplex.GetObjective().Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = it.Value;
}
// Linear constraints.
// The derivative of a linear constraint ax - b (<)= 0 is just a.
for (int i = 0; i < linear.Length; ++i)
{
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)linear[i].Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = kktsum[it.NumVar] - rpi[i] * it.Value;
}
}
// Quadratic constraints.
// The derivative of a constraint xQx + ax - b <= 0 is
// Qx + Q'x + a.
for (int i = 0; i < quad.Length; ++i)
{
for (ILinearNumExprEnumerator it = ((ILinearNumExpr)quad[i].Expr).GetLinearEnumerator();
it.MoveNext(); /* nothing */)
{
kktsum[it.NumVar] = kktsum[it.NumVar] - qpi[i] * it.Value;
}
for (IQuadNumExprEnumerator it = ((IQuadNumExpr)quad[i].Expr).GetQuadEnumerator();
it.MoveNext(); /* nothing */)
{
INumVar v1 = it.NumVar1;
INumVar v2 = it.NumVar2;
kktsum[v1] = kktsum[v1] - qpi[i] * xmap[v2] * it.Value;
kktsum[v2] = kktsum[v2] - qpi[i] * xmap[v1] * it.Value;
}
}
// Bounds.
// The derivative for lower bounds is -1 and that for upper bounds
// is 1.
// CPLEX already returns dj with the appropriate sign so there is
// no need to distinguish between different bound types here.
for (int j = 0; j < x.Length; ++j)
{
kktsum[x[j]] = kktsum[x[j]] - cpi[j];
}
foreach (INumVar v in x)
{
if (System.Math.Abs(kktsum[v]) > ZEROTOL)
{
throw new System.SystemException("Stationarity test failed at " + v
+ ": " + System.Math.Abs(kktsum[v]));
}
}
// KKT conditions satisfied. Dump out the optimal solutions and
// the dual values.
System.Console.WriteLine("Optimal solution satisfies KKT conditions.");
System.Console.WriteLine(" x[] = " + arrayToString(xval));
System.Console.WriteLine(" cpi[] = " + arrayToString(cpi));
System.Console.WriteLine(" rpi[] = " + arrayToString(rpi));
System.Console.WriteLine(" qpi[] = " + arrayToString(qpi));
}
catch (ILOG.Concert.Exception e)
{
System.Console.WriteLine("IloException: " + e.Message);
System.Console.WriteLine(e.StackTrace);
retval = -1;
}
finally
{
if (cplex != null)
{
cplex.End();
}
}
System.Environment.Exit(retval);
}
