Sentence examples for by the gap function from inspiring English sources

After this, by the gap function, the equivalence between two kinds of optimization problems is obtained.

Now, by using the gap function ({vartheta_{alpha}}(x)), we obtain an error bound result for (GMVE).

In this section, we shall transform the bilevel variational inequalities (1) and (2) into a one-level variational inequality by the gap functions of (LVI) and (UVI).

By virtue of the gap function, sufficient conditions for the H-continuity and B-continuity of the solution mapping of the (PGVQVLIP) are also derived.

By virtue of the gap function, sufficient conditions for the H-continuity and B-continuity of the solution mapping S of (PGVQVLIP) are also derived.

Later, by the definition of the gap function for Minty vector variational inequalities, some differential and sensitivity results for Minty vector variational inequalities were also obtained in [10].

In fact, the representation of the gap function by smoothening and using a higher-order distance field are very similar, see Fig. 12. Assume the existence of a contact frame C being defined as a surface which serves for parametrizing the contacting domain in three-dimensional two-body contact with local coordinate ξ ˆ ∈ R 2. All quantities referring to the contact frame are denoted by.

Usually, the gap function is defined by the closest point projection between points on the contactor surface C (1 ) to the target boundary, i.e. (21) g ˆ = x ˆ (2 ) - x ˆ (1 ) T ν ˆ where the vector ν ˆ is the normal to the tangential plane at the projection point x ˆ (2 ) and pointing outwards.

The presence of a significant 3rd AF J3 adds interesting effect on the gap function.

The gap function assumes smoothness of the contact boundaries.

They also obtained an explicit expression of the contingent derivative for a class of set-valued maps, and some optimality conditions for (VVI) and weak (VVI) by virtue of the gap functions.