Optimization and Hessian Matrix Calculations
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syms K L
[K,L]=meshgrid(0:0.1:10);
Q=10*(K1/4)*(L1/2);
mesh(K,L,Q)
contour(K,L,Q)
meshc(K,L,Q)
syms K L;
Q=10*(K1/4)*(L1/2);
diff(Q,K)
hessiana=jacobian(jacobian(Q,[K,L]),[K,L])
subs(hessiana,[K,L],[2,1])
syms x y;
f=4*x2+y2+2*x*y-3*x-y+1;
[x,y]=solve(diff(f,x),diff(f,y),x,y)
syms x y;
hessiana=jacobian(jacobian(f,[x,y]),[x,y])
eig(hessiana)
vpa(ans)
syms x y lambda;
f=x2+y2-2*x-x*y+5;
L=f-lambda*(x+y-1);
[lambda,x,y]=solve(diff(L,lambda),diff(L,x),diff(L,y),lambda,x,y)
syms x y lambda;
hessiana=jacobian(jacobian(L,[x,y]),[x,y])
eig(hessiana)