Solver4J – Newton equality constrained with feasible starting point

The class NewtonLEUnconstrainedFSP 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 $x \in dom f$ with $Ax = b$

Code example

Consider the following convex problem:

${minimize}_{x} x - \log (- x^{2} + 1)$ with
$dom f = {x | x^{2} < 1}$

It can be solved like this:

		// Objective function
		ConvexMultivariateRealFunction objectiveFunction = new ConvexMultivariateRealFunction() {
			
			public double value(DoubleMatrix1D X) {
				double x = X.getQuick(0);
				return x - Math.log(1-x*x);
			}
			
			public DoubleMatrix1D gradient(DoubleMatrix1D X) {
				double x = X.getQuick(0);
				return F1.make(new double[]{1+2*x/(1-x*x)});
			}
			
			public DoubleMatrix2D hessian(DoubleMatrix1D X) {
				double x = X.getQuick(0);
				return F2.make(new double[][]{{4*Math.pow(x, 2)/Math.pow(1-x*x, 2)+2/(1-x*x)}});
			}
			
			public int getDim() {
				return 1;
			}
		};

		OptimizationRequest or = new OptimizationRequest();
		or.setCheckKKTSolutionAccuracy(true);
		or.setF0(objectiveFunction);
		or.setInitialPoint(new double[] {0});//must be feasible
		
		// optimization
		NewtonLEConstrainedFSP opt = new NewtonLEConstrainedFSP();
		opt.setOptimizationRequest(or);
		opt.optimize();

This will give the solution (that we expect):

				double[] sol = opt.getOptimizationResponse().solution;
				sol[0] = 1-Math.sqrt(2);

Download test source bundle

Download the entire test source bundle from here.