regularized_norm_tradeoff.m
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regularized_norm_tradeoff.m
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			% Builds a norm minimization tradeoff curve
			%
			% This script solves a family of problems of the form
			% minimize \|\| Ax-b \|\|_1 + gamma \|\| x \|\|_Inf
			% for varying values of gamma. For gamma = 0, this is simply an
			% unconstrained norm minimization; for gamma = Inf, x = 0 and
			% \|\| A x - b \|\| = \|\| b \|\| are optimal. Varying gamma allows us
			% to genreate a tradeoff curve between these extremes.

			n = 10;
			A = randn(2*n,n);
			b = randn(2*n,1);
			gamma = logspace( -1, 3 );
			nrms = zeros( size( gamma ) );
			xnrms = zeros( size( gamma ) );
			fprintf( 1, 'Gamma: ' );
			for k = 1 : length( gamma ),
			if k > 1 && rem( k, 10 ) == 1, fprintf( 1, '\n ' ); end
			fprintf( 1, '%g ', gamma( k ) );
			cvx_begin quiet
			variable x(n)
			minimize( norm( A * x - b, 1 ) + gamma( k ) * norm( x, Inf ) )
			cvx_end
			nrms( k ) = norm( A * x - b, 1 );
			xnrms( k ) = norm( x, Inf );
			end
			fprintf( 1, 'done.\n' );
			figure
			semilogx( gamma, nrms );
			xlabel( '\gamma' );
			ylabel( '\|\| A * x - b \|\|_1' );
			figure
			plot( xnrms, nrms );
			xlabel( '\|\| x \|\|_{\infty}' );
			ylabel( '\|\| A * x - b \|\|_1' );