PROBLEM 3


function F = Dfun(x)

F=[ 
    x(1)^2+x(2)^2+x(3)^2+x(4)^2-2
    x(1)+x(3)-x(2)-x(4)
    x(1)*x(3)+x(2)*x(4)
    x(2)+2*x(3)-3*x(4)];


>> x=fsolve(@Dfun,[1 1 1 1], optimset('Display','iter'))

                                         Norm of      First-order   Trust-region
 Iteration  Func-count     f(x)          step         optimality    radius
     1          5               8                             6               1
     2         10           0.962            0.6           0.63               1
     3         11           0.962            1.5           0.63             1.5
     4         16        0.624117          0.375          0.426           0.375
     5         21        0.549772         0.9375           1.92           0.938
     6         26      0.00407976       0.240966          0.138           0.938
     7         31    6.73783e-007      0.0271066        0.00171           0.938
     8         36    2.25591e-014     0.00036652      3.13e-007           0.938
Optimization terminated successfully:
 First-order optimality is less than options.TolFun.

x =

    1.1325    0.8162   -0.1325    0.1838




EXTRA CREDIT


function F = myfun2(x)
F=[ 
    x(1)^2+x(2)^2+x(3)^2+x(4)^2-5
    x(1)+x(3)-x(2)-x(4)+1
    x(1)*x(3)+x(2)*x(4)
    x(2)+2*x(3)-3*x(4)];


>> x=fsolve(@myfun2,[1 1 1 1], optimset('Display','iter'))

                                         Norm of      First-order   Trust-region
 Iteration  Func-count     f(x)          step         optimality    radius
     1          5               6                             1               1
     2         10         5.50488           0.25           1.18               1
     3         15         5.17324        0.15069           1.03               1
     4         20         2.78724              1           3.23               1
     5         25        0.668495       0.891381           2.77             2.5
     6         30      0.00126802       0.182677          0.109             2.5
     7         35    9.77783e-009     0.00944636       0.000288             2.5
     8         40    7.85913e-019   2.81582e-005      2.56e-009             2.5
Optimization terminated successfully:
 First-order optimality is less than options.TolFun.

x =

    1.3798    1.6899   -0.3798    0.3101