Page 376 - Applied Numerical Methods Using MATLAB

PROBLEMS 365

(P7.7.2a)
(b1) Max x x 1 x 2 x 3
subject to the constraints

   
0
x 1
0
x 1 x 2 + x 2 x 3 + x 3 x 1 = 3and x =  x 2  ≥   (P7.7.2b)
x 3 0
Try the routine “fmincon()” with the initial guesses listed in
Table P7.7.

(b2) Min x x 1 x 2 x 3 (P7.7.3a)
subject to the constraints (P7.7.2b).
Try the routine “fmincon()” with the initial guesses listed in
Table P7.7.
(P7.7.4a)
(c1) Max x x 1 x 2 + x 2 x 3 + x 3 x 1
subject to the constraints
   
x 1 0
0
x 1 + x 2 + x 3 = 3and x =  x 2  ≥   (P7.7.4b)
x 3 0
Try the routine “fmincon()” with the initial guesses listed in
Table P7.7.

(c2) Min x x 1 x 2 + x 2 x 3 + x 3 x 1 (P7.7.5a)
subject to the constraints (P7.7.4b).
Try the routine “fmincon()” with the initial guesses listed in
Table P7.7.
10000
(d) Min x 2 (P7.7.6a)
x 1 x
2
subject to the constraints

0
x 1
2
2
x + x = 100 and x = > (P7.7.6b)
1 2
x 2 0
Try the routine “fmincon()” with the initial guesses listed in
Table P7.7.
(e) Does the routine work well with all the initial guesses? If not, does it
matter whether the starting point is inside the admissible region?
(cf) Note that, in order to solve the maximization problem by “fmincon()”, we
have to reverse the sign of the objective function. Note also that the objective
functions (P7.7.3a) and (P7.7.5a) have infinitely many minima having the value
f(x) = 0 in the admissible region satisfying the constraints.