Journal of Convex Analysis 31 (2024), No. 3, 733--748
Copyright Heldermann Verlag 2024
Existence and Stability for Generalized Polynomial Vector Variational Inequalities
Tran Van Nghi
Hanoi Pedagogical University 2, Hanoi, Vietnam
tranvannghi@hpu2.edu.vn
Nguyen Nang Tam
(1) Institute of Theoretical and Applied Research, Duy Tan University, Hanoi, Vietnam
(2) Faculty of Natural Sciences, Duy Tan University, Da Nang, Vietnam
nguyennangtam@duytan.edu.vn
We investigate the generalized polynomial vector variational inequality (GPVVI), which is a natural generalization of generalized polynomial variational inequality (GPVI) and vector variational inequality (VVI). Due to the scalarization method, which is a powerful technique in vector optimization, we establish a relationship between the Pareto solution sets of the GPVVI and the solution set of the GPVI. By using the concept on exceptional family of elements, recession cone, and positive semi-definiteness of matrices, we present sufficient conditions for the nonemptiness and boundedness of the Pareto solution sets of the GVVI. We present sufficient conditions for the upper/lower semicontinuity of the weak Pareto solution map and the stability for GVVIs. Finally, we obtain some applications to polynomial variational inequality. The presented result develops and complements the previous ones.
Keywords: General vector variational inequality, Pareto solution, solution existence, stability, upper/lower semicontinuity.
MSC: 90C29, 90C31, 90C33, 54C60, 49J40, 49J53, 49K40.
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