eucl_proj_cone1.m
de096106547amaster

eucl_proj_cone1.m
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			% Euclidean projection on the nonnegative orthant
			% Section 8.1.1, Boyd & Vandenberghe "Convex Optimization"
			% Joelle Skaf - 10/07/05
			%
			% The projection of x0 on the proper cone K = R+^n is given by
			% minimize \|\| x - x0 \|\|^2
			% s.t. x >= 0
			% It is also given by: P_K(x0)_k = max{x0_k,0}

			% Input data
			randn('seed',0);
			n = 10;
			x0 = randn(n,1);

			fprintf(1,'Computing the analytical solution...');

			% Analytical solution
			pk_x0 = max(x0,0);

			fprintf(1,'Done! \n');

			% Solution via CVX
			fprintf(1,'Computing the solution via a QP...');

			cvx_begin quiet
			variable x(n)
			minimize ( norm(x - x0) )
			x >= 0;
			cvx_end

			fprintf(1,'Done! \n');

			% Verification
			disp('-----------------------------------------------------------------');
			disp('Verifying that the analytical solution and the solution obtained via QP are equal: ');
			[pk_x0 x]
			disp('They are equal as expected!');