function K = mink(phi0,m0,n0)
% minimizes F(k) = Psi(k) - <phi,k>
% we'll be using the smoothed version
global phi m n a
m=m0; n=n0;
phi = phi0;
%a = 1;

%K = randn(size(phi))';

%K = graddesc(K,phi);
%K = fmincon(@myobj,K,[],[],[],[],-ones(size(K)),ones(size(K)));

get_ccgenerators

return

function get_ccgenerators
% tries to get the generators for the convex cone
global G phi
%G = [];
%K = randn(size(phi))';
%%K = zeros(size(phi))'; 
%%i = randel(1:length(K));
%%K(i) = rand-.5;
%G = fmincon(@myobj,K,[],[],[],[],-ones(size(K)),ones(size(K)));
G = -eye(length(phi));
while 1
  K = randn(size(phi))';
  %K = K/max(abs(K));
  %i = randel(1:length(K));
  %K = zeros(size(phi))'; 
  %K(i) = rand-.5
  %K(i) = 2*flip-1;
  K = fmincon(@myobjG,K,[],[],[],[],-ones(size(K)),ones(size(K)));
  G = [G, K];
  pinds = convhullinds(G)
  G = G(:,pinds);
end
return

function y = myobjG(K)
global phi G
y = F(K,phi);
% want K to be far from all elements in G
KK = repmat(K,[1,size(G,2)]);
y = y - 0.001*sum(sum((G-KK).^2));
return


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


function f = F(K,phi)
global m n
f = Psi(K,m,n) - phi*K;
%f = Psi(K,m,n);
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