A note on the existence of solutions to the semi-affine variational inequalities problems
DOI:
https://doi.org/10.56764/hpu2.jos.2024.3.2.35-45Abstract
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.
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