Sentence examples for using the nonlinear scalarization from inspiring English sources

It is worth mentioning that it is possible to obtain the same conclusion using the nonlinear scalarization function (xi_{e}).

Now, by using the nonlinear scalarization technique, we propose some sufficient conditions for Hölder continuity of the solution mapping for (PGVQEP).

Finally, we apply the nonlinear scalarization function to discuss the weak -sharp minimizer in vector optimization problems.

The following lemma characterizes some of the important properties of the nonlinear scalarization mapping which are used in the sequel.

Namely, by using the properties either of the Minkowski functional (q_{e}) or the nonlinear scalarization function (xi_{e}) (in particular their monotonicity), some scholars have made a conclusion that many fixed point results in the setting of cone metric spaces or tvs-cone metric spaces can be directly obtained as a consequence of the corresponding results in metric spaces (see [1 12]).

Recall that the nonlinear scalarization function is defined by (2.2).

In this paper, by the nonlinear scalarization method, we study a global error bound of (WVVI).

Given a fixed point and, the nonlinear scalarization function is defined by (3.26).

In what follows, we present several properties about the nonlinear scalarization function.

In Section 3, we discuss a global error bound of (WVVI) by the nonlinear scalarization method.

In this section, we introduce the nonlinear scalarization mapping and some of its important properties.