![]() ![]() In each iteration of the Simplex Method it assumes the following:Īt any point in the Simplex Method, excluding the basis where the Optimal Solution is obtained, the Dual is infeasible. Strong Duality is where the Dual and Primal have the same optical objective function output where the Duality Gap is equal to zero. Likewise, the opposite of the above is true if we swap the words of primal with dual and dual with primal. If we translate that to the dual at this very same phase in the pivot, it will be infeasible as some constraint condition will be violated (more will be explained on this shortly). In order for the Primal to be unbounded, and the Dual be infeasible, we need to have an available pivot in the objective function row, but the entire $A_j$ column of that pivot be either negative or zero. ![]() Take note that the latter answer gives a model that you can play around with yourself to test to see if its trueĪfter asking my professor, and looking into it more, I finally found something that may make this problem make more sense and would answer your question: Here’s another example where the the both questions you proposed has been answered. Weak and Strong Duality in Linear Programming.Difference between weak duality and strong duality?.Here are some more helpful links to explore weak and strong duality and their differences: Note, the proof they have there is actually pretty good. ![]() This fundamentally boils down to the weak duality theorem which has been answered here with a similar question. Likewise, if a primal is unbounded, then its dual is infeasible. If a dual is unbounded, then its primal is infeasible. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |