移动渐近线法

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 = 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). %

function [xmmaymmazmmalamxsietamuzetslowupp] = ...
mmasub（mniterxvalxminxmaxxold1xold2 ...
f0valdf0dxdf0dx2fvaldfdxdfdx2lowuppa0acd）;
%
%    Written in May 1999 by
%    Krister Svanberg 
%    Department of Mathematics
%    SE-10044 Stockholm Sweden.
%
%    Modified （“spdiags“ instead of “diag“） April 2002
%
%
%    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（ij） = 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（ij） = 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