Search results
Results from the WOW.Com Content Network
By definition, strong duality holds if and only if the duality gap is equal to 0. This is opposed to weak duality (the primal problem has optimal value smaller than or equal to the dual problem, in other words the duality gap is greater than or equal to zero).
The strong duality theorem says that if one of the two problems has an optimal solution, so does the other one and that the bounds given by the weak duality theorem are tight, i.e.: max x c T x = min y b T y. The strong duality theorem is harder to prove; the proofs usually use the weak duality theorem as a sub-routine.
So, in short: weak duality states that any solution feasible for the dual problem is an upper bound to the solution of the primal problem. Weak duality is in contrast to strong duality, which states that the primal optimal objective and the dual optimal objective are equal. Strong duality only holds in certain cases. [2]
These are the best funny quotes to make you laugh about life, aging, family, work, and even nature. Enjoy quips from comedy greats like Bob Hope, Robin Williams, and more. 134 funny quotes that ...
Image credits: girlposts.co In the US, the commonly thrown around number is that a woman makes 84 cents to each dollar paid to a man. Again, this might seem like a smallish gap, but once you ...
The duality gap is zero if and only if strong duality holds. Otherwise the gap is strictly positive and weak duality holds. [5] In computational optimization, another "duality gap" is often reported, which is the difference in value between any dual solution and the value of a feasible but suboptimal iterate for the primal problem.
50. "I just want women to always feel in control. Because we're capable, we're so capable." — Nicki Minaj. 51. "You draw your own box. You introduce yourself as who you are. . . .
In optimization problems in applied mathematics, the duality gap is the difference between the primal and dual solutions. If is the optimal dual value and is the optimal primal value then the duality gap is equal to . This value is always greater than or equal to 0 (for minimization problems).