%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%????????????Developed?by?Bapi?Chatterjee?IIT?Delhi?India???????????????%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%?The?script?steepest.m?optimizes?a?multivariable?function?using?steepest
%?descent?method.
%?Input:
%???????1）Dimensionality?of?the?multivariable?function.
%???????2）Function?in?the?proper?format.
%?????????Note:?Kindly?ensure?that?the?function?is?entered?in?the?proper
%?????????format?readable?by?MATLAB.?This?is?the?only?point?where?the
%?????????maximum?possibility?of?error?is?there.
%???????3）Initial?approximation?vector.
%?????????Note:?Kindly?ensure?that?the?dimensionalty?matches?with?the
%?????????dimension?of?initial?approximation?vector.
%???????4）Error?tolerance.
%
%?For?the?theory?of?steepest?decent?method?see?“Practical?methods?of
%?optimization-?R.?Fletcher?Second?edition?2003?John?Wiley?&?Sons“?or
%?any?other?good?book?on?unconstrained?optimization?methods.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp（‘Would?you?like?to?clear?your?workspace?memory?and?command?screen?‘）;
z=input（‘To?do?so?enter?1?any?other?number?to?continue:‘）;
if?z==1
????clc;clear
end
choice=input（‘To?do?a?maximization?enter?1?for?minimization?enter?2:‘）;a=2;
while?a==2
????if?choice~=1&&choice~=2
????????disp（‘Wrong?input!‘）;a=2;
????????choice=input（‘To?do?a?maximization?enter?1?for?minimization?enter?2:‘）;
????else
????????a=1;
????end
end
a=2;
mark=0;
flag=0;
count=0;
syms?b;
u=[];
warning?off?all

try
????while?a==2
????????n=floor（input（‘Enter?the?dimension?of?function:‘））;
????????if?n<1
????????????disp（‘Kindly?enter?a?positive?integer‘）;a=2;
????????else
????????????a=1;
????????end
????end
catch
????disp（‘Kindly?enter?a?positive?integer‘）;
end
a=2;
for?i=1:n
????syms?（[‘x‘?num2str（i）]）;
end
while?a==2
????try
????????f=input（‘Enter?the?function?in?terms?of?variables?x_i（i.e.?x1x2etc.）:‘）;a=1;
????catch
????????disp（‘Kindly?recheck?the?index?of?variables?and?format?of?expression!‘）;a=2;
????end
end
if?choice==1
????f=-f;
end
x0=input（‘Enter?the?initial?approximation?row?vector?of?variables:‘）;a=2;
while?a==2
????if?length（x0）~=n
????????disp（‘The?dimension?of?initial?approximation?is?incorrect!‘）;a=2;
????????x0=input（‘Enter?the?initial?approximation?as?row?vector?of?variables:‘）;
????else
????????a=1;
????end
end
try
????eps=abs（input（‘Enter?the?error?tolerance:‘））;
catch
????disp（‘Kindly?enter?a?real?number!‘）;
end
g=f;
try
????for?i=1:n
????????h（i）=diff（g[‘x‘?num2str（i）]）;
????????for?j=1:n
????????????k（ij）=diff（h（i）[‘x‘?num2str（j）]）;
????????end
????end
catch
????disp（‘Your?optimization?problem?can?not?be?solved‘）;
????return
end
disp（‘Hessian?matrix?of?the?function=‘）
if?choice==1
????disp（-k）
elseif?choice==2
????disp（k）
end
for?i=1:n
????for?j=1:n
????????if?i==j
??????????

?屬性????????????大小?????日期????時間???名稱
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?????文件???????8987??2019-06-04?10:45??steep.m

????I..D...?????????0??2019-06-04?10:50??親測可用

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?????????????????8987????????????????????2