analytic_center.m
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analytic_center.m
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			% Section 8.5.3: Analytic center of a set of linear inequalities
			% Boyd & Vandenberghe "Convex Optimization"
			% Joëlle Skaf - 04/29/08
			%
			% The analytic center of a set of linear inequalities and equalities:
			% a_i^Tx <= b_i i=1,...,m,
			% Fx = g,
			% is the solution of the unconstrained minimization problem
			% minimize -sum_{i=1}^m log(b_i-a_i^Tx).

			% Input data
			randn('state', 0);
			rand('state', 0);
			n = 10;
			m = 50;
			p = 5;
			tmp = randn(n,1);
			A = randn(m,n);
			b = Atmp + 10rand(m,1);
			F = randn(p,n);
			g = F*tmp;

			% Analytic center
			cvx_begin
			variable x(n)
			minimize -sum(log(b-A*x))
			F*x == g
			cvx_end

			disp(['The analytic center of the set of linear inequalities and ' ...
			'equalities is: ']);
			disp(x);