A note on the existence of solutions to the semi-affine variational inequalities problems

  • Van-Dong Vu
Từ khóa: Semi-affine variational inequalities, finite-dimensional Hilbert space, solution existence, recession cone, normal cone

Tóm tắt

The semi-affine variational inequality problem offers a general and versatile framework applicable to many problems in economics, mathematical physics, operations research, and mathematical programming. One of the important applications of the semi-affine variational inequality problem is quadratic programming. It is well-known that the first-order necessary optimality condition for a constrained optimization problem can be rewritten as a variational inequality. This paper investigates the existence of solutions for the semi-affine variational inequality problem in the finite-dimensional Hilbert spaces. Under suitable conditions, we show that the solution set of the semi-affine variational inequality problem is nonempty. The obtained results contribute to and complement the existing literature.

điểm /   đánh giá
Phát hành ngày
2024-08-30