Determination of Optimal Vertices From Feasible Solutions in Unimodular Linear P
Determination of Optimal Vertices From Feasible Solutions in Unimodular Linear P
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□ As a special case of the above theorem, we get the following useful result.
Corollary 3 Let x° e Gx and (y°, 2°) G Fy^. If {x°)'^ z° 1/2. In case the problem (P) has a unique optimal solution x* € S-, ;, we can compute each coordinate of the optimal solution by (3).
Proof: If x^ is integral. Theorem 2(a) implies that x* = [xjj for an x* ^ Sx- So we only consider the case where Xj is not integral. If x^ — [x°J 1/2 > (x°)^z° = c^x° - 6^y°.
Since 6 y° is a lower bound of t;*, by Theorem 2(c), ...there exists x* G 5^ such that i^ = [x^J . If x°- - |_x^J > 1/2, we have Xj — [XjJ > 1/2 >[x)z=cx— by.
Hence, by Theorem 2(b), there exists x' G S^ such that ij = \xj]. □ Theorem 2 gives information about an element of an optimal solution. The next theorem shows a relation between a feasible solution and coordinates of an optimal solution.
Theorem 4 Let x° G Gx, and let v* be the optimal value of (P).
What to read after Determination of Optimal Vertices From Feasible Solutions in Unimodular Linear P?
You can find similar books in the "Read Also" column, or choose other free books by Shinji Mizuno to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
□ As a special case of the above theorem, we get the following useful result.
Corollary 3 Let x° e Gx and (y°, 2°) G Fy^. If {x°)'^ z° 1/2. In case the problem (P) has a unique optimal solution x* € S-, ;, we can compute each coordinate of the optimal solution by (3).
Proof: If x^ is integral. Theorem 2(a) implies that x* = [xjj for an x* ^ Sx- So we only consider the case where Xj is not integral. If x^ — [x°J 1/2 > (x°)^z° = c^x° - 6^y°.
Since 6 y° is a lower bound of t;*, by Theorem 2(c), ...there exists x* G 5^ such that i^ = [x^J . If x°- - |_x^J > 1/2, we have Xj — [XjJ > 1/2 >[x)z=cx— by.
Hence, by Theorem 2(b), there exists x' G S^ such that ij = \xj]. □ Theorem 2 gives information about an element of an optimal solution. The next theorem shows a relation between a feasible solution and coordinates of an optimal solution.
Theorem 4 Let x° G Gx, and let v* be the optimal value of (P).
What to read after Determination of Optimal Vertices From Feasible Solutions in Unimodular Linear P?
You can find similar books in the "Read Also" column, or choose other free books by Shinji Mizuno to read onlineMoreLess
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