Seminar: “A Strongly Convergent Algorithm for Bilevel Split Variational Inequalities with Quasimonotone Operators”

Thời gian: 14:00 ngày 05/10/2026.
Địa điểm: Phòng Lab Toán ứng dụng, tầng 12 Nhà A1, ĐHKTQD.
Người trình bày: PGS.TS Nguyễn Thị Thu Thủy
Nội dung: 

• The talk focuses on the development of an iterative algorithm for solving bilevel split variational inequality problems (BSVIPs) involving quasimonotone operators. Such problems combine two levels of variational inequalities together with a split constraint, and therefore arise as challenging extensions of classical variational inequality and split feasibility problems.
• The main objective is to establish strong convergence of the proposed iterative sequence to a solution of the bilevel split variational inequality problem. In contrast to many existing methods that require monotonicity, Lipschitz continuity, or other restrictive assumptions on the underlying operators, the proposed approach works under the weaker quasimonotonicity condition.
• The algorithm is designed by incorporating suitable projection and correction mechanisms to handle both the upper- and lower-level variational inequalities as well as the split structure. The convergence analysis relies on tools from Hilbert-space theory, including projection properties, Fejér-type estimates, and appropriate assumptions ensuring that the generated sequence converges strongly to a desired solution.
• The talk also discusses the advantages and limitations of the proposed method, together with numerical experiments illustrating its effectiveness and computational performance. Overall, the results contribute to the development of strongly convergent algorithms for broader classes of non-monotone variational inequality problems and provide a useful framework for related applications in optimization and equilibrium problems.

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