Is it possible for a linear programming optimization problem possible to have a degenerate optimal solution whereas the dual has a unique optimal solution? I can't find a scenario where this is possible but intuitively it seems that it is possible. The answer is yes, but only if there are other optimal solutions than the degenerate one.
For example, suppose the primal problem is. So we do have a situation with a degenerate optimal solution in the primal but a unique dual optimal. However, if the degenerate optimal solution is unique, then there must be multiple optimal solutions in the dual.
If an optimal solution is degenerate, then a There are alternative optimal solutions b The solution is infeasible c The solution is of no use to the decision- maker d None of the above.
Proof 1: 1 Consider a minimization LP in standard form. If there exits a nondegenerate optimal bfs for this LP,then the dual LP will have a unique optimial solution. Proof 2: 2 consider a minimization LP in standard form. If the primal LP has a unique optimal solution,then the dual LP will have a non-degenerate optimal solution.
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The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Primal- degenerate optimal, Dual - unique optimal Ask Question. Asked 10 years ago. Active 7 years, 6 months ago. Viewed 12k times. Mike Spivey GBa GBa 2 2 gold badges 11 11 silver badges 16 16 bronze badges.
Active Oldest Votes. Primal Optimal Solution Dual Optimal Solution a Multiple implies Degenerate b Unique and nondegenerate implies Unique and nondegenerate c Multiple and nondegenerate implies Unique and degenerate d Unique and degenerate implies Multiple. Mike Spivey Mike Spivey If there are other solutions, then yes math. But why is the converse true? Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password.Everyone was so very accommodating.
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