Geodesic
A penalty approach for a box constrained variational inequality problem
Applications of Mathematics, Tome 63 (2018) no. 4, pp. 439-454 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2018.0334-17
Classification : 47J20, 65J15, 65K10, 65K15, 90C33
Keywords: box constrained variational inequality problem; power penalty approach; strongly monotone operator 
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     title = {A penalty approach for a box constrained variational inequality problem},
     journal = {Applications of Mathematics},
     pages = {439--454},
     year = {2018},
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Kebaili, Zahira; Benterki, Djamel. A penalty approach for a box constrained variational inequality problem. Applications of Mathematics, Tome 63 (2018) no. 4, pp. 439-454. doi: 10.21136/AM.2018.0334-17

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