svm-direction.m

function [xMin, fMin, t, nIter, infoPD] = PrimalDual(F, ineqConstraint, eqConstraint, x0, lambda0, nu0, mu, tol, tolFeas, maxIter, opts)
% Initilize the structures 
nIter = 0;
stopCond = false;
x_k = x0; %k stands for current iteration
lambda_k = lambda0; %k stands for current iteration
nu_k = nu0; %k stands for current iteration
infoPD.xs = x_k; %all the interations
infoPD.lambdas = lambda0; %all the iterations of lambdas
infoPD.nus = nu0; %all iterations of nus
infoPD.r_dual = []; 
infoPD.r_cent = [];
infoPD.r_prim = [];
infoPD.surgap = [];

% Define residual function
r_dual = @(t, x, l, n) F.df(x) + (ineqConstraint.df(x))'*l + eqConstraint.A'*n;
r_cent = @(t, x, l, n) -diag(l)*ineqConstraint.f(x) - ones(m, 1)/t;
r_prim = @(t, x, l, n) eqConstraint.A*x - eqConstraint.b;
res = @(t, x, l, n) [r_dual(t, x, l, n); r_cent(t, x, l, n); r_prim(t, x, l, n)];

% Surrogate gap to track how much we need to step
eta = - (ineqConstraint.f(x0))'*lambda0;
t = mu*m/eta;

% Find direction we need to go 
while (~stopCond && nIter < maxIter) %check if stopping criteria are not violated

    % Compute residual at current iteration
    res_k = res(t, x_k, lambda_k, nu_k);
    disp(size(res_k))
    
    % Find direction (inverted r_t for deltaY)
    HessianIneqConstraints_x_k = zeros(length(x_k),length(x_k));
    ineqConstraints_x_k = ineqConstraint.d2f(x_k); 
    % Compute the Hessian of the current iteration for x_k
    HessianIneqConstraints_x_k = zeros(length(x_k),length(x_k));
    inequalityConstraints_x_k = ineqConstraint.d2f(x_k); 
    for j = 1:length(l_k)
      HessianIneqConstraints_x_k = HessianIneqConstraints_x_k + lambda_k(j)*inequalityConstraints_x_k(:,:,j);
    end
      
    deltaY = -[F.d2f(x_k) + HessianIneqConstraints_x_k,  ineqConstraint.df(x_k)'    , eqConstraint.A'; ...
               -diag(l_k)*ineqConstraint.df(x_k)       , -diag(ineqConstraint.f(x_k)), zeros(m, nEq)  ; ...
               eqConstraint.A                          ,  zeros(nEq, m)              , zeros(nEq, nEq)]\res_k;