bounded_iso.m

y = [0.1 0.2 0.1 0.2 0.5 0.4 0.6 0.7 0.8]';
p = length(y);
a = 0.2; b = 0.6;
A = tril(toeplitz([-1 1 zeros(1,p-2)]));
cvx_begin
variable x(p, 1)
minimize norm(x - y)
subject to
A * x <= 0
x(1) >= a
x(p) <= b
cvx_end

[x pava(y)]
%ans =
%
%    0.2000    0.1000
%    0.2000    0.1500
%    0.2000    0.1500
%    0.2000    0.2000
%    0.4500    0.4500
%    0.4500    0.4500
%    0.6000    0.6000
%    0.6000    0.7000
%    0.6000    0.8000