al_main.m

Augmented Lagrangian Algorithms 求解非线性最化的局部最优解

%this code just fornonlinear equality constraints augmented Langrangian algorithms
%for the inequality constraints , we could add some nonnegative slack %variables to turn them into the equality constraints
%perface
%start condition
%'this codt for nonlinear equality  and inequality constraints augmented Langrangian algorithms');
%'for the inequality constraints , we could add some nonnegative slack variables  
%'please write the obj function in the obj.m,   the constrains function in the constrains.m ');
%'pena;%penalty parameter;c_scale;%scale parameter;e_al;%tolerance', are kebian);
%'you can change them in the AL_main.m');
%'please put in the start point x_al_start  the r_al_start, and the opt_newton, where opt1==1 DFP and golden, or ==2 BFGS and wolfe );
% the N_equ is the number of equality, the N_inequ, is the number of the inequality 
%'function  f=AL_main( x_al_start, r_al_start, N_equ, N_inequ, opt1 )');
function  [X,FVAL]=AL_main(x_al)
%==============initial the program========================
global r_al pena N_equ N_inequ;
%r_al=[1,1,1]
%N_equ=1;
%N_inequ=2;
strong=0;
pena=10;%penalty parameter;
c_scale=2;%scale parameter;
cta=0.5; %cta ( 0, 1 )
e_al=0.005;%tolerance
max_itera=25;
out_itera=1;% out iteration
% the start ponit
%x_start=(x_al, r_al);
N_x_al=max( size( x_al));
N_r_al=max( size( r_al));

%=====================start the iteration======================
while  out_itera < 26    
    
    x_al0=x_al;
    r_al0=r_al;
    compare0=compare(x_al0);
    %quasi_newton
    [X,FVAL]=fminsearch(@AL_obj,[1,1,1]);
    x_al=X;    %get  the  new  x
         
    % check the stop condition
    %if norm( constrains( x_al ) ) < e_al
    if compare( x_al ) < e_al
        disp('we get the opt point:');
        break
    end
    
    %constrains  think over!!!!!!!!!!!!!1 
    if  compare( x_al ) < cta * compare0  
        %% pena=pena
    else
        pena=min(1000, c_scale*pena);%% the max pena is 1000;
        disp(' pena=10*pena '); 
    end
        
    %change the r_al
    %% where is the equality part
    N=N_equ+N_inequ;
    temp_constrains=constrains( x_al );
    for i=1:N
        %% the equality constrains part;
        if N_equ~=0 && N_equ>=i        
            r_al(i)=r_al(i) - pena*temp_constrains(i);
        end
        %% the inequality constrains part;
        if N_inequ~=0 && i>N_equ       
           r_al(i)=max( 0, ( r_al(i)-pena*temp_constrains(i)));
        end
    end
    
    if strong==1     
        if  compare( x_al) > compare0 %%% not descend 
            x_al=x_al0;
            r_al=r_al0;
            disp('@@@@@@@ouccer constrains(x)>constrains(x0), but  get the fit point!!!!!!@@@@@@');
            break
        end
    end
    
   % if  obj( x_al ) > obj( x_al0 )
   %    disp('@@@@@@@ouccer obj(x)>obj(x0), but  get the fit point!!!!!!@@@@@@');
   %    break
   %end
   
    out_itera=out_itera+1;
    out_itera
    [x_al,r_al]
    [compare( x_al),obj(x_al)]
   % disp('the value of constrains ');
   % norm( constrains( x_al ) )  
end

%++++++++++++the iteration end ++++++   
%disp('x_al=');
%x_al
disp('!!!!!!!!!!!!!!!!!the iteration over!!!!!!!!!!!!!!!!!!!!!!');
disp('iteration of the out');
out_itera
disp('the value of the obj function');
obj( x_al )
disp('the value of constrains ');
compare( x_al )
disp('the opt point');
r_al
X=x_al;
FVAL=obj(X);
% opt_valu( x_al )