function?[x?itr]?=?ALH（?x?f?g?G?H?Dg?Hg?e?k?eta）
%AUGMENTED_LAGRANGIAN
itr?=?0;????????????		%initialize?iteration?counter
numV?=?length（x）;???????????%?number?or?variables
numC?=?size（g（x）?1）;??????%?number?of?constraints?/?dual?variables
y?=?zeros（numC?1?）;?????????%Lagrange?multipliers

ALk?=?@（x）（f（x）?-?y‘*g（x）?+?0.5*k*（norm（g（x）））^2）;??	%?Augmented?Lagrangian
DALk?=?@（x）（G（x）?-?Dg（x）*y?+?k*Dg（x）*g（x））;?????????	%?gradient?of?Augmented?Lagrangian

%Hessian?of?Augmented?Lagrangian
????function?HA?=?HALk（x）
????????HA?=?H（x）+?k*Dg（x）*Dg（x）‘;
????????for?i?=?1:numC
????????????HA?=??HA?-?Hg{i}（x）*y（i）?+?k*Hg{i}（x）*gi（i）;??????????????????????????%?hessian?of?AL
????????end
????end

while?（norm（g（x））?>=?e）
????gi?=?g（x）;
????
????[x?nsteps]?=?newton（x?ALk?DALk?@HALk?e?eta?true）;
????y?=?y?-?k?*?g（x）;
????
????itr?=?itr?+?1;
????fprintf（?‘Iteration:?%d?Newton?Steps:?%d?Constraint?Violation:?%s?x:?%s?\n‘?itr?nsteps?num2str（g（x）‘）?num2str（x‘））;
end

fprintf（‘Augmented?Langragian?method\n‘）;
fprintf（‘Number?of?Iterations:??%d\n‘?itr）;
for?i?=?1:numV
????fprintf（‘x（%d）:????????????%8.4f\n‘?i?x（i））;
end
fprintf（‘f（x）:????????????%8.4f\n‘?f（x））;

fprintf（‘g（x）:????????????%s\n‘?num2str（g（x）‘））;
fprintf（‘k:????????????%f\n‘?k）;
end

function?[x?itr]?=?newton（x?f?G?H?e?eta?isprint）
itr?=?0;????????????%initialize?iteration?counter
numV?=?length（x）;???%?number?or?variables

%Computation?loop
while?norm（G（x））?>?e
????%?primal?regularization
????lambda?=?1e-5;
????[~p]?=?chol（（H（x）?+?lambda?*?eye（numV?）））;
????while?p?~=?0
????????lambda?=?10?*?lambda;
????????[~p]?=?chol（（H（x）?+?lambda?*?eye（numV?）））;
????end
????
????dxs?=??-（（H（x）?+?lambda?*?eye（numV?））\G（x））;
????alpha?=?1;
????
????while?（（f（x?+?alpha?*?dxs）?-?f（x））?>=?eta?*?alpha?*?G（x）‘?*dxs）;
????????alpha?=?alpha/2;
????end
????
????x?=?x?+?alpha?*?dxs;
????itr?=?itr?+?1;??%counter+1
????if?isprint
????????fprintf（?‘Iteration:?%d?f（x）:?%f?x:?%s?e:?%f?\n‘?itr?f（x）?num2str（x‘）?e）;
????end
end
end

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????4259??2015-11-13?20:16??拉格朗日\AL.zip
?????文件????????2085??2012-10-28?08:40??拉格朗日\ALH.m
?????文件????????1317??2013-04-11?09:35??拉格朗日\license.txt
?????文件????????3772??2008-09-01?14:52??拉格朗日\multiplier.f90
?????文件????????1835??2012-10-25?10:50??拉格朗日\newton_constrained.m
?????文件????????2143??2012-10-25?09:48??拉格朗日\prob1.m
?????文件????????2278??2012-10-28?08:41??拉格朗日\prob2.m
?????目錄???????????0??2015-11-16?20:57??拉格朗日\