Solver4J – Newton equality constrained with infeasible starting point

The class NewtonLEUnconstrainedISP implements a (linear) equality constrained Newton optimizer (see S.Boyd and L.Vandenberghe, "Convex Optimization", p. 521 for more details), and can be used to solve the following problem:

${minimize}_{x} f (x)$ s.t.
$Ax = b$

where $f : R^{n} \to R$ is convex and twice differentiable, and $A \in R^{p x n}$ with $rank A = p < n$ , given a starting point $x \in dom f$ .

Code example

Consider the following quadratic problem:

${minimize}_{x} \frac{1}{2} x^{T} Px + q^{T} x + r$ s.t.
$Ax = b$
where $P = \frac{0.01522}{2} (\begin{matrix} 1.68 & 0.34 & 0.38 \\ 0.34 & 3.09 & - 1.59 \\ 0.38 & - 1.59 & 1.54 \end{matrix})$ , $q = (\begin{matrix} - 0.018 \\ - 0.025 \\ - 0.01 \end{matrix})$ , $r = 0$
and $A = (\begin{matrix} 1 & 1 & 1 \end{matrix})$ , $b = (\begin{matrix} 1 \end{matrix})$

It can be solved like this:

		
		//commons-math client code
		RealMatrix Pmatrix = new Array2DRowRealMatrix(new double[][] { 
				{ 1.68, 0.34, 0.38 },
				{ 0.34, 3.09, -1.59 }, 
				{ 0.38, -1.59, 1.54 } });
		RealVector qVector = new ArrayRealVector(new double[] { 0.018, 0.025, 0.01 });

		// Objective function
		double theta = 0.01522;
		RealMatrix P = Pmatrix.scalarMultiply(theta);
		RealVector q = qVector.mapMultiply(-1);
		PDQuadraticMultivariateRealFunction objectiveFunction = new PDQuadraticMultivariateRealFunction(P.getData(), q.toArray(), 0);

		OptimizationRequest or = new OptimizationRequest();
		or.setF0(objectiveFunction);
		or.setInitialPoint(new double[] { 0.1, 0.1, 0.1 });//LE-infeasible starting point
		or.setA(new double[][] { { 1, 1, 1 } });
		or.setB(new double[] { 1 });

		// optimization
		NewtonLEConstrainedISP opt = new NewtonLEConstrainedISP();
		opt.setOptimizationRequest(or);
		opt.optimize();

This will give the solution:

				double[] sol = opt.getOptimizationResponse().solution;
				sol[0] = 0.04632311556;
				sol[1] = 0.50863084610;
				sol[2] = 0.44504603834;

Download test source bundle

Download the entire test source bundle from here.