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The Microsoft Solver Foundation provides some excellent APIs for solving optimization problems in C# .NET. Getting to documentation about the Quadratic Programming facilities can be a bit tricky though. I’ve added below some sample code to help out with this.

In the following example I’m solving an example of the lagrangian dual form used for classification in an SVM.

// Classify using solver
InteriorPointSolver solver = new InteriorPointSolver();

// Langrangian Dual
int dual = 0;
solver.AddRow("L", out dual);

// Sum Constraint
int linearConstraint = 0;
solver.AddRow("SumConstraint", out linearConstraint);

// Add variables and Lagrangian linear terms
int[] vars = new int[n];
for (int i = 0; i < n; i++)
{
	// Add the variable
	solver.AddVariable("a" + i, out vars[i]);

	// Factor in C upper bounds
	solver.SetBounds(vars[i], 0, C);
}

// Linear constraint must equal 0
solver.SetBounds(linearConstraint, 0, 0);

// Lagrangian Quadratic Terms
for (int i = 0; i < n; i++) { 	solver.SetCoefficient(linearConstraint, vars[i], trainingData[i].output()); 	solver.SetCoefficient(dual, vars[i], 1); 	Parallel.For(0, n, o, (int j) =>
	{
		double coef = trainingData[i].output() * trainingData[j].output() *
			kernel.evaluate(trainingData[i].point(), trainingData[j].point());

		solver.SetCoefficient(dual, -0.5 * coef, vars[i], vars[j]);
	});
}

solver.AddGoal(dual, 0, false);

InteriorPointSolverParams param = new InteriorPointSolverParams();

Essentially all we are doing here is adding all the variables to our constraint optimization problem and asking the solver to minimize. The vars array simply expressing a list of identifier for variables in the constraint problem. You should fire up the Solver Foundation library and give it a shot yourself.

Here are some resources that should make understanding this a bit easier as well. Its the official blog of one of the key developers on the project, specifically the links to tutorial on the quadratic programming solver.

Nathan Brixius’ QP Solver Tutorial