Please Check the Solution is right or not 5.23 Strong duality in linear programm

Question

Please Check the Solution is right or not

5.23 Strong duality in linear programming. We prove that strong duality holds for the LP minimize subject to Azb and its dual maximize subject to AT2+ c = 0, z 0, provided at least one of the problems is feasible. In other words, the only possible excep- tion to strong duality occurs when p*-oo and d* =-oo (a) Suppose p* is finite and x is an optimal solution. (If finite, the optimal value of an LP is attained.) Let I {1,2, . .. , m} be the set of active constraints at x* Show that there exists a z R" that satisfies iEI Show that z is dual optimal with objective value c' Hint. Assume there exists no such z, ie.,-c g {elziai I zi > 0). Reduce this to a contradiction by applying the strict separating hyperplane theorem of example 2.20, page 49, Alternatively, you can use Farkas' lemma (see §5.8.3) (b) Suppose po and the dual problem is feasible. Show that d-oo. Hint. Show 0, bTu

Explanation / Answer

Yes, the solution for all parts look goood enough in accordance with the questions.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---