Example 4 We continue with the previous example. X (1 , 2 , 2 , 2 , 1) is defined as (24). If we apply an interative method (e.g., the interior point method) to solve (10), µ may converge toward zero along the path. However, the objective function is ill-defined when µ is zero. Therefore, we define a new objective function as (25). Then, (9) can be reformulated as (26). 21 such that min ξ , x ,µ, ζ , $_{ω}$L ( µ, ω ) (A) ω$_{i}$ ≥ − z$_{i}$e ζ$_{i}$ for ∀ i (B) ζ$_{i}$ ≥ α ∑ J j =1 [ x$_{j}$ A$_{ij}$ − Q$_{j}$ ( A $^{T}$ξ ) j − B$_{j}$b$_{j}$ ( x$_{j}$ − Q$_{j}$ ) ] , ∀ i (C) ζ$_{i}$ ≥ α J j $_{=1}$[ x$_{j}$ A$_{ij}$ − B$_{j}$b$_{j}$x$_{j}$ ], ∀ i (D) µ ≥ 0 (E) ξ ≥ 0 (F) N ∑ i =1 ξ$_{i}$ = 1 (G) ( x , ξ ) ∈ F (26) L ( µ, ω ) = µ ln ( ∑ N i $_{=1}$θ$_{i}$ e$^{ω}$ i µ ) if µ > 0 max$_{1}$$_{≤}$$_{i}$$_{≤}$$_{N}$ ω$_{i}$ if µ = 0 (25) X (1 , 2 , 2 , 2 , 1) = { x ∈ R $^{7}$| x$_{1}$ = x$_{5}$ = x$_{6}$ = x$_{7}$ = 0 . 001 , 0 ≤ x$_{2}$, x$_{3}$, x$_{4}$ ≤ 0 . 001 } (24) 4.3.2 The Pseudo-Code