Solver4J – QP - quadratic programming

A minimization problem in the form of:

  minimize_x (1/2)x^TPx+q^Tx+r  s.t.
    Gx ≤ h
    Ax = b,

where P ∈ S₊ⁿ, G ∈ R^mXn and A ∈ R^pXn

is called a quadratic program (QP). In a quadratic program we minimize a (convex) quadratic objective function with affine constraint functions. Quadratic programs include linear program as a special case by taking P=0.

2D example

Consider the problem graphically represented hereafter:

It can be solved like this:

		
		// Objective function
		double[][] P = new double[][] {{ 1., 0.4 }, { 0.4, 1. }};
		PDQuadraticMultivariateRealFunction objectiveFunction = new PDQuadraticMultivariateRealFunction(P, null, 0);

		//equalities
		double[][] A = new double[][]{{1,1}};
		double[] b = new double[]{1};

		//inequalities
		ConvexMultivariateRealFunction[] inequalities = new ConvexMultivariateRealFunction[2];
		inequalities[0] = new LinearMultivariateRealFunction(new double[]{-1, 0}, 0);
		inequalities[1] = new LinearMultivariateRealFunction(new double[]{0, -1}, 0);
		
		//optimization problem
		OptimizationRequest or = new OptimizationRequest();
		or.setF0(objectiveFunction);
		or.setInitialPoint(new double[] { 0.1, 0.9});
		//or.setFi(inequalities); //if you want x>0 and y>0
		or.setA(A);
		or.setB(b);
		or.setToleranceFeas(1.E-12);
		or.setTolerance(1.E-12);
		
		//optimization
		Solver4J opt = new Solver4J();
		opt.setOptimizationRequest(or);
		opt.optimize();

This will give the solution:

				double[] sol = opt.getOptimizationResponse().solution;
				sol[0] = 0.5
				sol[1] = 0.5

Download test source bundle

Download the entire test source bundle from here.