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Keywords:
box constrained variational inequality problem; power penalty approach; strongly monotone operator
box constrained variational inequality problem; power penalty approach; strongly monotone operator
Summary:
We propose a penalty approach for a box constrained variational inequality problem $(\rm BVIP)$. This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of $\rm BVIP$ when the function $F$ involved is continuous and strongly monotone and the box $C$ contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results tested on some examples are satisfactory and confirm the theoretical approach.
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