Research Article

Homotopy Method for a General Multiobjective Programming Problem under Generalized Quasinormal Cone Condition

Table 1

Results for Example 4.2.

𝑥 ( 0 ) 𝑥 𝑓 ( 𝑥 ) 𝐻 𝜔

(1.0000, 2.0000, 0.0000, 1.0000, 1.0000) ( 1 . 3 0 7 4 , 2 . 8 6 0 5 , 1 . 0 4 7 0 , 0 . 4 1 0 3 , 0 . 4 4 7 5 ) ( 1 1 . 3 5 6 6 , 9 . 2 9 4 2 ) 1 . 0 𝑒 0 1 2
(−1.0000, −2.0000, 1.0000, 1.0000, 1.0000) ( 1 . 3 0 7 3 , 2 . 8 6 0 3 , 1 . 0 4 7 0 , 0 . 4 1 0 2 , 0 . 4 4 7 6 ) ( 1 1 . 3 5 5 0 , 9 . 2 9 3 6 ) 1 . 0 𝑒 0 1 3

Now, we compare the same example with the one in [9] under the same initial point.

𝑥 ( 0 ) 𝑥 𝑓 ( 𝑥 ) 𝐻 𝜔

(1.0000, 2.0000, 0.0000, 1.0000, 1.0000) ( 0 . 3 0 7 7 , 0 . 5 3 7 4 , 0 . 2 7 0 3 , 0 . 1 3 3 6 , 0 . 2 8 0 4 ) ( 0 . 5 3 3 0 , 2 . 0 8 7 3 ) 6 . 6 𝑒 0 1 6
(−1.0000, −2.0000, 1.0000, 1.0000, 1.0000) ( 2 . 2 1 2 4 , 2 . 0 3 8 3 , 0 . 8 2 4 1 , 0 . 5 2 0 8 , 8 . 8 5 2 8 ) ( 8 8 . 3 7 1 5 , 1 9 . 2 2 4 6 ) 4 . 1 𝑒 0 1 4