function?[x_kf_k]=conjugate_gradient（funx0eps）
%%?Usage:[x_kf_k]=conjugate_gradient（‘x1^2+2*x2^2-4*x1-2*x1*x2‘[1;1]0.01）

x_k=x0;
l=length（x0）;
f=inline（sym（fun））;
%?每次新初始點處
g0=G（funx_k）;?%這里s_k是1*2矩陣
s_k=-g0;
k=0;

while?1
????%?精確一維搜索表達式，fun_v
????syms?x;
????switch?l
????????case?2fun_v=f（x_k（1）+s_k（1）*xx_k（2）+s_k（2）*x）;
????????case?3fun_v=f（x_k（1）+s_k（1）*xx_k（2）+s_k（2）*xx_k（3）+s_k（3）*x）;
????????case?4fun_v=f（x_k（1）+s_k（1）*xx_k（2）+s_k（2）*xx_k（3）+s_k（3）*xx_k（4）+s_k（4）*x）;
????end
????fun_vv=inline（fun_v）;
????
????%?調用Newton法求最小lamda值
????c=Advance_Back（fun_v）;
????result=Newton（fun_vvc）;
????lamda=result（1）;
????x_k=x_k+lamda*s_k;
????g1=G（funx_k）;???%這里是k+1的梯度值
????
????norm_g1=norm（g1）;
????if?norm_g1????????switch?l
????????????case?2f_k=f（x_k（1）x_k（2））;
????????????case?3f_k=f（x_k（1）x_k（2）x_k（3））;
????????????case?4f_k=f（x_k（1）x_k（2）x_k（3）x_k（4））;
????????end
????????return
????end
????
????u_k1=norm（g1）^2/norm（g0）^2;
????s_k=-g1+u_k1*s_k;
????k=k+1;
????g0=g1;?%g1退化為g0
????
????if?k==l-1
????????%x_k=x_k;?x0=x_k;
????????g0=G（funx_k）;?%這里s_k是1*2矩陣
????????s_k=-g0;
????????k=0;
????end
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%?函數2，精確一維搜索Newton法
function?x1=Newton（funx0）?%x1可能是多個值
delta?=0.01;
%%?求表達式的一階導d1_f，二階導d2_f
d1_f=inline（diff（sym（fun）））;
d2_f=inline（diff（sym（fun）2））;

%%?計算牛頓迭代公式
while?1
????d1_x0=d1_f（x0）;
????d2_x0=d2_f（x0）;
????err=abs（d1_x0）;
????
????if?err?????????x1=x0;
????????return
????end
????x0=x0-d1_x0/d2_x0;??%計算新x0
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%?函數3，求梯度矩陣函數
function?[Gradient_f]=G（funx）;
%%?表達式中變量個數
l=length（x）;
Gradient_f=zeros（l1）;
%%?梯度矩陣（在x處一階導）的值
for?i=1:l
????%?循環求出梯度表達式
????x_i=[‘x‘num2str（i）];
????d=diff（sym（fun）x_i）;????%對x（i）求梯度
????%?將xi替換為x（i）
????for?k=1:l
????????x_k=[‘x‘num2str（k）];
????????x_k1=[‘x（‘num2str（k）‘）‘];
????????d=strrep（char（d）x_kx_k1）;
????end
????%?將該字符串寫成內聯函數，并將計算的值賦給Gradient_f矩陣對應的位置
????d_fun=inline（d）;
????Gradient_f（i）=d_fun（x）;
????
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%?函數4，進退法確定牛頓搜索初始點
function?c=Advance_Back（fun）

t0=0;
h=0.1;

%%?求函數表達式
f=inline（fun）;
f_t0=f（t0）;
t2=t0+h;
f_t2=f（t2）;

if?f_t2<=f_t0???%向正方探測
????t1=t0+h;
????f_t1=f（t1）;
else????????????%向負方向探測
????h=-h;
????t1=t0+h;
????f_t1=f（t1）;
end
%%?進退法計算
while?1
????if?f_t1<=f_t0
????????h=2*h;
????????t2=t0;
????????t0=t1;
????????t1=t0+h;
????????f_t1=f（t1）;
????else
????????if?t1????????????a=t1;
????????????b=t2;
????????else
????????????a=t2;
????????????b=t1;
????????end
????????c=（a+b）/2;
????????return;
????end
end

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2012-12-04?13:20??算法程序\
?????目錄???????????0??2012-12-04?12:48??算法程序\實用最優化方法2\
?????文件????????3144??2012-12-04?15:03??算法程序\實用最優化方法2\DFP.m
?????文件?????????810??2012-12-04?09:35??算法程序\實用最優化方法2\G.m
?????文件????????1399??2012-12-04?09:59??算法程序\實用最優化方法2\G_H.m
?????文件????????3075??2012-12-04?15:00??算法程序\實用最優化方法2\conjugate_gradient.m
?????文件????????3585??2012-12-04?15:02??算法程序\實用最優化方法2\damp_Newton.m
?????文件????????3201??2012-12-04?15:03??算法程序\實用最優化方法2\gradient_my.m
?????目錄???????????0??2012-12-04?13:18??算法程序\實用最優化算法\
?????文件????????1092??2012-12-04?13:09??算法程序\實用最優化算法\Advance_Back.m
?????文件????????1307??2012-12-04?13:11??算法程序\實用最優化算法\Bisect.m
?????文件????????1361??2012-12-04?13:12??算法程序\實用最優化算法\Golden_Slect.m
?????文件????????2003??2012-12-04?13:13??算法程序\實用最優化算法\Inaccuracy.m
?????文件????????1097??2012-12-04?13:15??算法程序\實用最優化算法\Newton.m
?????文件????????1117??2012-12-04?13:17??算法程序\實用最優化算法\Succeed_Fail.m
?????文件???????40960??2012-11-04?10:09??算法程序\實用最優化算法\測試記錄.doc
?????文件???????25581??2012-11-04?10:09??算法程序\實用最優化算法\測試記錄.docx