function kavitaineq(n)
% trying to lower-bound \sum_i a_i b_i
% where a_i, b_i are in [0,1] 
% want a bound of the form
% \sum_i a_i b_i \geq \psi(a) \sum_i b_i
% where \psi:[0,1]^n\to [0,1] 
%% is non-decreasing in each component.
% a completely trivial psi is 0.
% a less trivial one is the one used by Marton:
% \psi(a) = min_i a_i
% can we get a tighter psi?

global myopt
myopt = optimset('Diagnostics','off');
myopt = optimset('Display','off');
warning off



global a BB YY


T = 500;
BB = [];
YY = [];
PROGstart(T)
for t=1:T
  
  % fix an a
  a = rand(n,1);

  LB = zeros(n,1);
  UB = LB + 1;
  for i=1:10
    b = rand(n,1);
    [b,y] = fmincon(@myobj,b,[],[],[],[],LB,UB);
  end
  if y > min(a) + 1e-7
    'heh'
    keyboard
  end
  
  %BB(end+1) = sum(b);
  %YY(end+1) = y;
  PROGupdate(t);
end
PROGend

return


function y = myobj(b)
global a
y = a'*b / sum(b);
return