Sentence examples for duality hold from inspiring English sources

If, in addition, the assumptions of weak duality hold for all feasible solutions ( x, μ, w, v, s, t, y ˜, p ) of (DM2), then ( x ∗, μ ∗, w ∗, v ∗, s ∗, t ∗, y ˜ ∗, p ∗ = 0 ) is an optimal solution of (DM2).

That duality held firm for much of the ensuing half century.

Hence -strong duality holds.

So, ϵ-strong duality holds.

that is, -weak duality holds.

Then the stable total Lagrange duality holds.

(In projective space geometry, duality holds for points and planes).

The stable strong duality holds between ((tilde{P})) and (D).

(ii) The strong duality holds between (P) and (D).

The strong duality holds between (P) and (D).

(i) The strong duality holds between ((tilde{P})) and (D).