Sentence examples for a weakly solution of 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 solution is called a weakly maximal solution of if.

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

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 ∗ ).

Hence ( x ∗, y ∗, z ∗, v ∗ ) is a weakly efficient solution of (D), and the efficient values of (FP) and (D) are clearly equal to their respective weakly efficient solution points.

If the hypotheses of Theorem  6 are fulfilled, then ( x ∗, y ∗, z ∗, v ∗ ) is a weakly efficient solution of (D) and their efficient values of (FP) and (D) are equal.

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

If (GNCI) holds at each feasible point x of (P), then u is a weakly efficient solution of (P).

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

Then is a weakly minimal solution of.

Since is a weakly minimal solution of,.