Can primal and dual both infeasible?
Primal feasible and bounded, dual infeasible is impossible: If the primal has an optimal solution, the duality theorem tells us that the dual has an optimal solution as well. In particular the dual is feasible. Primal unbounded and dual feasible and bounded is impossible: Assume that AT y = c has a solution y.
Can a linear program and its dual both be infeasible?
A LP can also be unbounded or infeasible. Duality theory tells us that: If the primal is unbounded, then the dual is infeasible; If the dual is unbounded, then the primal is infeasible.
Can an LP be unbounded and infeasible?
A linear program is infeasible if its feasibility set is empty; otherwise, it is feasible. A linear program is unbounded if it is feasible but its objective function can be made arbitrarily “good”.
Can the dual be unbounded?
Both the primal and dual are feasible and not unbounded (hence have optimal solution).
What is primal and dual problem?
In the primal problem, the objective function is a linear combination of n variables. In the dual problem, the objective function is a linear combination of the m values that are the limits in the m constraints from the primal problem.
How do you convert primal to dual?
Use your textbook for detail explanation….1. Rules & Example-1.
| In Primal | Then in Dual | |
|---|---|---|
| 1. | Objective function is maximum | Objective function is minimum |
| 2. | x1 unrestricted in sign | 1st constraint is = type |
| 3. | 1st constraint is = type | y1 unrestricted in sign |
| 4. | constraint is ≤ type | constraint is ≥ type |
What is primal and dual in linear programming?
Any LP problem (either maximization and minimization) can be stated in another equivalent form based on the same data. The new LP problem is called dual linear programming problem or in short dual. In general, it is immaterial which of the two problems is called primal or dual, since the dual of the dual is primal.
What is the difference between unbounded and infeasible?
An infeasible problem is a problem that has no solution while an unbounded problem is one where the constraints do not restrict the objective function and the objective goes to infinity. Both situations often arise due to errors or shortcomings in the formulation or in the data defining the problem.
Can minimization problems be unbounded?
For the standard minimization linear program, the constraints are of the form ax+by≥c, as opposed to the form ax+by≤c for the standard maximization problem. As a result, the feasible solution extends indefinitely to the upper right of the first quadrant, and is unbounded.
Can a primal be feasible and bounded at the same time?
If the primal is feasible and bounded, then the dual must also be feasible and bounded and they must have the same optimal objective value (this follows from strong duality for linear programming). So the conclusion in your case is that the dual must have been misformulated.
What are the relations between primal and dual?
Relations between Primal and Dual. If the primal problem is Maximize ctx subject to Ax = b, x ‚ 0 then the dual is Minimize bty subject to Aty ‚ c (and y unrestricted) Easy fact: If x is feasible for the primal, and y is feasible for the dual, then.
Are there any primal and dual optimal solutions?
• primal and dual optimal solutions are not necessarily unique • any combination of primal and dual optimal points must satisfy zi(bi−aT i x)=0, i =1,…,m in other words, for all i, aT i x < bi, zi =0 or a.
Which is the optimal value for the dual?
The dual has optimal solution a=7/11, b=3/11 and optimal objective value -27/11, which is exactly the optimal primal objective value.