Sentence examples for qualification condition from inspiring English sources

To proceed this way by using the conventional results of the generalized differential calculus [13] requires the fulfillment of the basic qualification condition, which reads in this case ∂ ( f − g ) ( x ∗, y ∗, z ∗ ) ∩ ( − N K ( x ∗, y ∗, z ∗ ) ) = ∅.

For z ∈ Sol ( P ), we assume that, under some constraint qualification condition (see [9]), there exists λ ∈ R + ( T ) such that 0 ∈ ∂ c f ( z ) + ∑ t ∈ T λ t ∂ c f t ( z ) + N ( C, z ), λ t f t ( z ) = 0, ∀ t ∈ T. (3.1).

Furthermore, (4.14) holds at ( x ∗, y ∗, z ∗ ) for the locally Lipschitzian function φ if we pass to the boundary of the normal cone in (4.13), that is, if the following qualification condition holds: ∂ ( f − g ) ( x ∗, y ∗, z ∗ ) ∩ ( − bd N K ( x ∗, y ∗, z ∗ ) ) = ∅, (4.15).

Note that in the fully convex (even nonsmooth) case, the assumption (4.4) in Theorem 4.1 can be replaced by a much weaker qualification condition [44] requiring that the set epi f ∗ + cone ( ⋃ i = 1 p epi g i ∗ ) is closed on R n × R m × R, where epi f ∗ denotes the conjugate function for an extended real-valued function f.

(ii) Let the solution map Ψ (4.1) be inner semicontinuous at ( x ∗, y ∗, z ∗ ) ∈ gph Ψ, and let the qualification conditions (4.4) and (4.14) hold at this point.

The second-order radial-asymptotic derivative, introduced in [20], was used in qualification conditions to consider the second-order proto-differentiability of the efficient solution map and the efficient frontier map of a parameterized vector optimization problem in [21].

In order to find the optimal solutions of the convex problem ( P ~ 1 ) by studying the Lagrange dual problem, some additional constraint qualification conditions must hold, beyond convexity, to ensure strong duality[23].

This paper presents the use of a reduced-order thermal model coupled with physics-of-failure-based life models to quantify the wear-out rates and life consumption for the dominant failure mechanisms under prospective in-service and qualification test conditions.

I'm far from the most religious guy out there, but the God I know loves and accepts EVERYONE without qualifications or conditions.

Only the federal government can pass Laws that establish the qualifications and conditions for professional practice, as subsequently occurred in 2008, when Law 11.889 was enacted.

The constraint qualification and optimality condition for the SOCBLP are studied in Section 4.