Sentence examples for continuity of the projection from inspiring English sources

By the continuity of the projection operator P K, and the upper semicontinuity of f, g and ε, it is clear to see that ψ is upper semicontinuous.

To prove this statement, consider a converging sequence to x ∗, then the continuity of the projection map and the continuity of the payoff function implies the continuity of the quantity (x_{i,t}frac {d_{i}}{Theta _{i,{t}}}).

Also from (14) and the Lipschitz continuity of the projection operator P K r with constant δ we have ∥ u n − u ∥ = ∥ u n − u − ( h ( u n ) − h ( u ) ) ∥ + ∥ P K r z n − P K r z ∥ = k ∥ u n − u ∥ + δ ∥ z n − z ∥, from which we have ∥ u n − u ∥ ≤ δ 1 − k ∥ z n − z ∥. (21).

Following the TS optimization, the minimum energy path (MEP) between the critical points were calculated with the nudged elastic band (NEB), to ensure continuity of the path and projection of the force, so that the system converges to the MEP.

This approach to relief sculpture preserves the continuity of the material's original surface and creates no projection from it.

Let us begin now, Yen [11] obtained the Hölder continuity of the unique solution of a classic perturbed variational inequality by the metric projection method.

In this section, we apply the variational characterization of the metric projection in Hilbert spaces to study the solvability of general variational inequalities without the continuity of the mappings involved in the considered general variational inequalities.

The most important difference is the continuity of the leadership.

"The concept was to restore the continuity of the narrative.

"There is continuity of the state," he told me recently.

Continuity of the house was more important than blood kinship.