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New smooth gap function for box constrained variational inequalities. (English) Zbl 1401.90244

Summary: A new smooth gap function for the box constrained variational inequality problem (VIP) is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47J20 Variational and other types of inequalities involving nonlinear operators (general)
65K05 Numerical mathematical programming methods

Software:

MCPLIB
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Full Text: DOI

References:

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