Sentence examples for by using some scalarization from inspiring English sources
Li and Wang [4] obtained a minimax inequality by using some scalarization functions.
By using the scalarization method, we transform the pessimistic semivectorial bilevel programming problem into a scalar objective optimization problem with inequality constraints.
Lin et al. [18, 19] investigated some bilevel minimax theorems and hierarchical minimax theorems for set-valued mappings by using nonlinear scalarization function.
By using conic scalarization, we will also propose a new formulation of trade-off for defining of properly efficient points based on conic scalarization.
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.
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.
Cheng and Zhu obtained a lower semicontinuity result of the solution mapping to weak vector variational inequalities in finite-dimensional spaces by using the scalarization method (see [14]).
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.
