This function mmasub performs one MMA-iteration, aimed at
% solving the nonlinear programming problem:
%
% Minimize f_0(x) + a_0*z + sum( c_i*y_i + 0.5*d_i*(y_i)^2 )
% subject to f_i(x) - a_i*z - y_i <= 0, i = 1,...,m
% xmin_j <= x_j <= xmax_j, j = 1,...,n
% z >= 0, y_i >= 0, i = 1,...,m
%*** INPUT:
%
% m = The number of general constraints.
% n = The number of variables x_j.
% iter = Current iteration number ( =1 the first time mmasub is called).
% xval = Column vector with the current values of the variables x_j.
% xmin = Column vector with the lower bounds for the variables x_j.
% xmax = Column vector with the upper bounds for the variables x_j.
% xold1 = xval, one iteration ago (provided that iter>1).
% xold2 = xval, two iterations ago (provided that iter>2).
% f0val = The value of the objective function f_0 at xval.
% df0dx = Column vector with the derivatives of the objective function
% f_0 with respect to the variables x_j, calculated at xval.
% df0dx2 = Column vector with the non-mixed second derivatives of the
% objective function f_0 with respect to the variables x_j,
% calculated at xval. df0dx2(j) = the second derivative
% of f_0 with respect to x_j (twice).
% Important note: If second derivatives are not available,
% simply let df0dx2 = 0*df0dx.
% fval = Column vector with the values of the constraint functions f_i,
% calculated at xval.
% dfdx = (m x n)-matrix with the derivatives of the constraint functions
% f_i with respect to the variables x_j, calculated at xval.
% dfdx(i,j) = the derivative of f_i with respect to x_j.
% dfdx2 = (m x n)-matrix with the non-mixed second derivatives of the
% constraint functions f_i with respect to the variables x_j,
% calculated at xval. dfdx2(i,j) = the second derivative
% of f_i with respect to x_j (twice).
% Important note: If second derivatives are not available,
% simply let dfdx2 = 0*dfdx.
% low = Column vector with the lower asymptotes from the previous
% iteration (provided that iter>1).
% upp = Column vector with the upper asymptotes from the previous
% iteration (provided that iter>1).
% a0 = The constants a_0 in the term a_0*z.
% a = Column vector with the constants a_i in the terms a_i*z.
% c = Column vector with the constants c_i in the terms c_i*y_i.
% d = Column vector with the constants d_i in the terms 0.5*d_i*(y_i)^2.
%
%*** OUTPUT:
%
% xmma = Column vector with the optimal values of the variables x_j
% in the current MMA subproblem.
% ymma = Column vector with the optimal values of the variables y_i
% in the current MMA subproblem.
% zmma = Scalar with the optimal value of the variable z
% in the current MMA subproblem.
% lam = Lagrange multipliers for the m general MMA constraints.
% xsi = Lagrange multipliers for the n constraints alfa_j - x_j <= 0.
% eta = Lagrange multipliers for the n constraints x_j - beta_j <= 0.
% mu = Lagrange multipliers for the m constraints -y_i <= 0.
% zet = Lagrange multiplier for the single constraint -z <= 0.
% s = Slack variables for the m general MMA constraints.
% low = Column vector with the lower asymptotes, calculated and used
% in the current MMA subproblem.
% upp = Column vector with the upper asymptotes, calculated and used
% in the current MMA subproblem.
