convex_interpolation.m
de096106547amaster

convex_interpolation.m
View Options

			% Figure 6.24: Fitting a convex function to given data
			% Section 6.5.5
			% Boyd & Vandenberghe "Convex Optimization"
			% Original by Lieven Vandenberghe
			% Adapted for CVX by Argyris Zymnis - 11/27/2005
			%
			% Here we find the convex function f that best fits
			% some given data in the least squares sense.
			% To do this we solve
			% minimize \|\|yns - yhat\|\|_2
			% subject to yhat(j) >= yhat(i) + g(i)*(u(j) - u(i)), for all i,j

			clear

			% Noise level in percent and random seed.
			rand('state',29);
			noiseint=.05;

			% Generate the data set
			u = [0:0.04:2]';
			m=length(u);
			y = 5(u-1).^4 + .6(u-1).^2 + 0.5*u;
			v1=u>=.2;
			v2=u<=.6;
			v3=v1.*v2;
			dipvec=((v3.u-.4ones(1,size(v3,2))).^(2)).*v3;
			y=y+40(dipvec-((.2))^2v3);

			% add perturbation and plots the input data
			randf=noiseint*(rand(m,1)-.5);
			yns=y+norm(y)*(randf);
			figure
			plot(u,yns,'o');

			% min. \|\|yns-yhat\|\|_2
			% s.t. yhat(j) >= yhat(i) + g(i)*(u(j) - u(i)), for all i,j
			cvx_begin
			variables yhat(m) g(m)
			minimize(norm(yns-yhat))
			subject to
			yhatones(1,m) >= ones(m,1)yhat' + (ones(m,1)g').(uones(1,m)-ones(m,1)u');
			cvx_end

			nopts =1000;
			t = linspace(0,2,nopts);
			f = max(yhat(:,ones(1,nopts)) + ...
			g(:,ones(1,nopts)).*(t(ones(m,1),:)-u(:,ones(1,nopts))));
			plot(u,yns,'o',t,f,'-');
			axis off
			%print -deps interpol_convex_function2.eps