eucl_proj_rect.m~
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eucl_proj_rect.m~
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			% Euclidean projection on a rectangle
			% Section 8.1.1, Boyd & Vandenberghe "Convex Optimization"
			% Joelle Skaf - 10/07/05
			%
			% The projection of x0 on a rectangle C = {x \| l <= x <= u} is given by
			% minimize \|\| x - x0 \|\|^2
			% s.t. l <= x <= u
			% It is also given by P_C(x0)_k = l_k if x0_k <= l_k
			% x0_k if l_k <= x0_k <= u_k
			% u_k if x0_k >= u_k

			cvx_quiet(true);
			% Input data
			n = 10;
			% generating vector l and u such that l < u
			l = -rand(n,1);
			u = rand(n,1);
			x0 = randn(n,1);

			% Analytical solution
			fprintf(1,'Computing the analytical solution ...');
			pc_x0 = x0;
			pc_x0(find(x0<=l)) = l(find(x0<=l));
			pc_x0(find(x0>=u)) = u(find(x0>=u));
			fprintf(1,'Done! \n');

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

			cvx_begin
			cv
			variable x(n)
			minimize ( norm(x-x0) )
			x <= u;
			x >= l;
			cvx_end

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

			% Verification
			disp('-----------------------------------------------------------------');
			disp('Verifying that the analytical solution and the solution obtained via QP are equal: ');
			[pc_x0 x]