DFP.m

function Return_Degeri = DFP(functname,dvar0,niter,tol,lowbound,intvl,ntrials)
% Optimization Theory
% Class Assignment  - DFP
% 27/12/2020


clc    
clf   
warning off 
   

e1 = 1.0e-04;               % convergence criteria
e2 = 1.0e-08; 
e3 = 1.0e-04;   
nvar = length(dvar0);       % number of variables



%% PLOTTING


if (nvar == 2)


  delx1 = 6;
  delx2 = 5;

    x1 = (dvar0(1)-delx1):0.1:(dvar0(1)+delx1);
    x2 = (dvar0(2)-delx2):0.1:(dvar0(2)+delx2);
	x1len = length(x1);
	x2len = length(x2);
	for i = 1:x1len
   	for j = 1:x2len
      	x1x2 =[x1(i) x2(j)];
      	fun(j,i) = feval(functname,x1x2);
   	end
	end

	c1 = contour(x1,x2,fun,[3.1 3.25 3.5 4 6 10 15 20 25],'k');
	    
	grid
	xlabel('x_1')
    ylabel('x_2')
    fname = strrep(functname,'_','-');
	title(strcat(' DFP: ',fname))

end




xs(1,:) = dvar0;
x = dvar0;
Lc = 'r';
fs(1) = feval(functname,x);             % Initial Value of Function
as(1)=0;
grad = (gradfunction(functname,x)); 

H = eye(nvar);                      
convg(1)=grad*grad';



for i = 1:niter-1
  
   fprintf('iteration number:  '),disp(i)
   d = (-H*grad')';                                                         % Search Direction
   
   output = GoldSection(functname,tol,x,d,lowbound,intvl,ntrials);          % Finding Alpha
   
   as(i+1) = output(1);
   fs(i+1) = output(2);
   for k = 1:nvar
      xs(i+1,k)=output(2+k);
      x(k)=output(2+k);
   end
   grad= (gradfunction(functname,x)) ;
   
   convg(i+1)=grad*grad';
   
   
   
   fprintf('objective function value:  '),disp(fs(i+1));
 
    
   
%% Plotting (drawing lines)
    
    
   if (nvar == 2)
      line([xs(i,1) xs(i+1,1)],[xs(i,2) xs(i+1,2)],'LineWidth',2,'Color',Lc)
      itr = int2str(i);
      x1loc = 0.5*(xs(i,1)+xs(i+1,1));
      x2loc = 0.5*(xs(i,2)+xs(i+1,2));
      
      
   if strcmp(Lc,'r') 
         Lc = 'b';
   else
         Lc = 'r';
   end
        
    pause(0.5)  
 
   end

   
   
%% DFP METHOD
   
if(convg(i+1)<= e3)                     % convergence criteria
    break; 
end


%*******************************************************

delx = (x - xs(i,:))';
Y = (grad -gradfunction(functname,xs(i,:)))'; 
Z = H*Y;
B = (delx*delx')/(delx'*Y);
C = -(Z*Z')/(Y'*Z);
H = H + B + C;
   
%********************************************************
end

len=length(as);
designvar=xs(length(as),:);
fprintf('\n Iterations:  '),disp(len-1)
fprintf('\n     x(1)      x(2)      F(x)\n')
% fprintf('\nThe design vector,function value \nduring the iterations\n')
disp([xs fs']);
Return_Degeri = [designvar fs(len)];