final commit

Author: ravichoudhary33

goldenSection.m

@@ -0,0 +1,73 @@
+clc
+clear
+close all
+%% declaring ackely function
+ackley = @(X,Y)-20 * exp(-0.2 * sqrt(0.5*(X.^2 + Y.^2))) - exp(0.5*(cos(2*pi*X) + cos(2*pi*Y))) + exp(1) + 20;
+
+%% golden section implementation
+% defining and declaring variables
+a = -5.0;
+b = 5.0;
+x = a:0.1:b;
+gammaInv = 0.618;
+L0 = b - a;
+L2_star = gammaInv.^2 * L0;
+x1 = a + L2_star;
+x2 = b - L2_star;
+n = 10;
+
+% ploting the function value with initial points
+figure(1)
+plot(x,ackley(x,0));
+title('golden section method on ackley function initial situation');
+xlabel('x');
+ylabel('f');
+hold on
+plot(a,ackley(a,0),'*k');
+plot(x1,ackley(x1,0),'*m');
+plot(x2,ackley(x2,0),'*r');
+plot(b,ackley(b,0),'*g');
+legend('f','a','x1','x2','b');
+hold off
+
+figure(2)
+plot(x,ackley(x,0));
+title('golden section method on ackley function final situation');
+xlabel('x');
+ylabel('f');
+hold on
+
+for j = 1:n
+   f1 = ackley(x1,0);
+   f2 = ackley(x2,0);
+   % checking unimodality condition and 
+   % assigning new a,x1,x2 and b accordingly
+   if f2 > f1
+       x3 = a + (x2 - x1);
+       b = x2;
+       x2 = x1;
+       x1 = x3;
+   elseif f1 > f2
+       x3 = x1 + (b - x2);
+       a = x1;
+       x1 = x2;
+       x2 = x3;
+   else
+      a = x1;
+      b = x2;
+      L0 = b - a;
+      L2_star = 0.382 * L0;
+      x1 = a + L2_star;
+      x2 = b - L2_star;
+   end
+end
+% plot the final point along with their function value
+plot(a,ackley(a,0),'*k');
+plot(x1,ackley(x1,0),'*m');
+plot(x2,ackley(x2,0),'*r');
+plot(b,ackley(b,0),'*g');
+legend('f','a','x1','x2','b');
+hold off
+% display the final interval
+Ln = [a b];
+display(Ln);

interiorPenalty.m

@@ -0,0 +1,63 @@
+clc
+clear
+close all
+%% defining three hump camel function
+three_hump_camel = @(X,Y) 2*X.^2 - 1.05*X.^4 + X.^6/6 + X.*Y + Y.^2;
+%% surface ploting three hump camel function
+[X,Y] = meshgrid(-5:.1:5, -5:.1:5);
+Z = three_hump_camel(X,Y);
+% display the surface plot of the function
+figure(1)
+surf(X,Y,Z)
+title('surface plot of three hump camel functoin');
+xlabel('x(1)');
+ylabel('x(2)');
+zlabel('threeHumpCamel');
+shading interp
+%% algorithm implementation
+phi_ = @(x,r) 2*x(1)^2 - 1.05*x(1)^4 + (x(1)^6)/6 + x(1)*x(2) + x(2)^2 - r * (1/(-x(1)-5) + 1/(-x(2)-5) + 1/(x(1)-5) + 1/(x(2)-5));
+% defining variables
+r = 1000.0;
+c = 0.01;
+epsilon = 0.005;
+options = optimoptions(@fminunc,'Algorithm','quasi-newton');
+% display contour plot and converging points
+figure(2)
+contour(X,Y,Z);
+title('contour of f(x,y) converges at black point');
+xlabel('x(1)');
+ylabel('x(2)');
+shading interp
+hold on
+% declaring initial point x1
+x1 = [-4.5, 2.5];
+f1 = three_hump_camel(x1(1), x1(2));
+scatter(x1(1),x1(2),'*');
+iteration = 0;
+% while function not converge keep iterating
+while true
+    iteration = iteration + 1;
+    phi = @(x)phi_(x,r);   
+    [x2,opt_phi] = fminunc(phi, x1, options);
+    f2 = three_hump_camel(x2(1), x2(2));
+    dx = x2 - x1;
+    quiver(x1(1),x1(2),dx(1),dx(2),0);
+    % convergence check
+    if abs((f2 - f1)/f2) <= epsilon
+        min_f = f2;
+        x_star = x2;
+        display('function Converged!');
+        fprintf('Number of Iteration taken to converge = %i\n', iteration);
+        fprintf('Minimum value of function = %f\n', min_f);
+        display('Optimal point is');
+        display(x_star);
+        scatter(x_star(1),x_star(2),'k*');
+        break
+    end
+    scatter(x2(1),x2(2),'*');
+    r = c * r;
+    x1 = x2;
+    f1 = f2;
+end
+legend('contour','intermediate point','direction of minima');
+hold off