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