Sentence examples for a weakly solution from inspiring English sources

Hence, (2.7), (2.9) and (2.11) imply that I ˜ ′ ( u n ) weakly converges to I ˜ ′ ( u ) in X ∗ and I ˜ ′ ( u ) = 0. So, it is not difficult to see that u ≥ 0 and I ′ ( u ) = I ˜ ′ ( u ) = 0, which means that u is a weakly solution of equation (1.1).

A feasible point is said to be a weak Pareto solution (a weakly efficient solution, a weak minimum) of (NMP) if there exists no other such that (1.9).

A feasible solution is called a weakly maximal solution of if.

A feasible solution x ∗ of (FP) is said to be a weakly efficient solution of (FP) if there does not exist any feasible solution x of (FP) such that ϕ ( x ) < ϕ ( x ∗ ).

Obviously, is a globally efficient solution of (VEPC), then is also a weakly efficient solution of (VEPC).

Since ( u, λ, μ ) is a feasible solution for (D), ( u, λ, μ ) is a weakly efficient solution for (D).

Let ( u, λ, μ ) be a weakly efficient solution of (D), and let a be a feasible solution of (P).

Proof Suppose, contrary to the result, that u is not a weakly efficient solution of (P).

Proof Suppose, contrary to the result, that x ¯ is not a weakly efficient solution for (CVP).

Proof Since x ¯ is a (weakly) efficient solution for (CVP), then by Lemma 3, x ¯ is a (weakly) efficient solution for (G-CVP).

Proof To prove the result by contradiction, suppose that x 0 is not a weakly efficient solution of (CSVVEP).