Sentence examples for using a scalarization method from inspiring English sources

Then, by using a scalarization method, we extend our main theorems to cone metric spaces.

Cheng and Zhu [5] obtained a result on the lower semicontinuity of the solution set map to a PVEP in finite-dimensional spaces by using a scalarization method.

By using a scalarization method, we obtain the lower semicontinuity of an approximate solution mapping for such a problem without the assumptions of monotonicity and compactness.

By using a scalarization method, Li and Li [19] discussed the Berge lower semicontinuity and Berge continuity of an approximate solution mapping for a parametric vector equilibrium problem.

By using a scalarization method, they obtained the lower semicontinuity of an approximate solution mapping for such a problem without the assumptions of monotonicity and compactness.

Then it is solved by using a scalarization method by Pascoletti and Serafini combined with an adaptive parameter control method based on sensitivity for the problem.

The code combines the multi-objective problem in a single objective by using a scalarization function of all the objective functions, as explained below.

By using a scalarization approach of Konnov [20], Li and Mastroeni [13] established error bounds for two kinds of (WVVI) with set-valued mappings.

By using a scalarization approach of Konnov [8], Li and Mastroeni [5] established the error bounds for two kinds of (WVVIs) with set-valued mappings.

It is worth mentioning that the results in this paper could not be derived from the corresponding results in the setting of metric spaces by using a scalarization function or a Minkowski functional.

In this work, we utilize a scalarization method to introduce a system of nonsmooth vector quasi-variational inequalities.