function [K,fval] = mink1(K0,bet0,m0,n0)
% minimizes F(k) = Psi(k) - <phi,k>
% we'll be using the smoothed version
global bet m n a oneb sig
m=m0; n=n0;
bet = bet0;
oneb = (bet > 0);
%a = 1;
sig = sign(K0);

K = randn(size(bet))';

%K = graddesc(K,phi);
for a=1:20
%for a=1
  [K,fval] = fmincon(@myobj,K,[],[],[],[],0*K0,ones(size(K)));
end
return


function y = myobj(K)
global oneb
y = F(K,oneb);
return


function f = F(K,bet)
global m n sig
f = spl(sum(sig.*K)) - bet*(sig.*K);
return


function nd = ndF(K,phi)
nd = Ndiff('mylocF',1,{K,phi});
nd = nd(:);
KND = [K nd]
return

function y = pl(x)
global m n a
y = x.*(x>0);
return


function y = spl(x)
global m n a
y = log(1+exp(a*x))/a;
return

function z = softmax(x,y)
z = x + pl(y-x);
return

function S = Psi1(K,m,n)
S1 = Psi( K,m,n);
S2 = Psi(-K,m,n);
S = softmax(S1,S2);
return

function S = Psi(K,m,n)
S = 0;
for t=1:n
  S = S + sum(pl(K));
  K = getK1(K,m,n-t+1);
end
return



function K = graddesc(K,phi)
d = 1;
mu = .95;
del0 = zeros(size(K));

goN = 1;
while goN
  %K = K/max(abs(K));
  nd = ndF(K,phi);
  del = d*nd + mu*del0;
  %K = K - del*nd;
  K = K - del;
  del0 = del;
  N = sum(abs(nd));
  goN = (N>0.0000001);
  f = F(K,phi);
  fprintf('F(k) = %1.9f \n',f);
end
return