lbfgs_infinity.cpp

#include <Eigen/Core>
#include <iostream>
#include <LBFGS.h>

using namespace std;
using namespace LBFGSpp;
using Eigen::Vector2d;
using Eigen::VectorXd;

int main() {

	LBFGSParam<double> param;
	param.max_iterations = 100;
	LBFGSSolver<double> solver(param);
	
	auto fun = [] (const VectorXd &x, VectorXd &grad) -> double {
		double mu = 0.0001;

		double fx = x(1);//sqrt(x(1));
		double a1 = 2;
		double b1 = 0;
		double a2 = -1;
		double b2 = 1;

		// c_i >= 0
		double c1 = x(1) - pow(a1*x(0)+b1, 3);
		double c2 = x(1) - pow(a2*x(0)+b2, 3);
		double c3 = x(1);

		fx += c1 > 0 ? -mu*log(c1) : std::numeric_limits<double>::infinity();
		fx += c2 > 0 ? -mu*log(c2) : std::numeric_limits<double>::infinity();
		fx += c3 > 0 ? -mu*log(c3) : std::numeric_limits<double>::infinity();

		grad = Vector2d(0., 1/* / sqrt(x(1))*/);

		grad += -mu/c1 * Vector2d(-3*pow(a1*x(0)+b1, 2), 1);
		grad += -mu/c2 * Vector2d(-3*pow(a2*x(0)+b2, 2), 1);
		grad += -mu/c3 * Vector2d(0.,1.);

		return fx;
	};

	VectorXd x = Vector2d(0., 100.);
	double fx;
	solver.minimize(fun, x, fx);

	cout << "fx = " << fx << endl;
	cout << "x = " << x << endl;
}