Sentence examples for generalized gap from inspiring English sources

In Section 2, we establish a global error bound of (VI) via the generalized gap functions.

We denote by D ( A, B ) : = ( D d 1 ( A, B ) ⋯ D d m ( A, B ) ), the generalized gap functional on  P ( X ). and by H ( A, B ) : = ( H d 1 ( A, B ) ⋯ H d m ( A, B ) ), the generalized Pompeiu-Hausdorff functional on  P ( X ).

When ϕ ( x, y ) = 1 2 ∥ x − y ∥ 2, the generalized regularized gap function reduces to the regularized gap function which was defined in [4].

Then we list some basic properties of the generalized regularized gap function f γ.

Furthermore we study various properties of the generalized regularized gap functions in random fuzzy mappings and derive the global error bounds for random generalized variational inequality problems.

Further, by using the generalized regularized gap function we obtain global error bounds of solutions of random generalized variational inequalities with and without a Lipschitz continuity assumption.

By using a generalized regularized gap function we calculated global error bounds, i.e., upper estimates on the distance to the solution set of random generalized variational inequality problems, which is one of the useful applications of gap functions.

One of such functions is a generalized regularized gap function [17] defined by f γ ( x ) : = − inf y ∈ K { 〈 f ( x ), y − x 〉 + γ φ ( x, y ) }, ∀ x ∈ R n, γ > 0, (1).

Recall the generalized regularized gap function for (WVVI) which is defined by ϕ γ ( x ) : = min ξ ∈ B e ∗ f γ ( x, ξ ), where f γ ( x, ξ ) = max y ∈ K { 〈 ∑ i = 1 m ξ i F i ( x ), x − y 〉 − γ φ ( x, y ) }.

The sets of putative orthologous target sequences were locally aligned with MAFFT (using option E-INS-i for generalized affine gap costs) (Katoh and Toh, 2008).

We propose truthful approximation mechanisms for strategic variants of the generalized assignment problem (GAP) in a payment-free environment.