A Computable Generalized Hessian of the D-Gap Function and Newton-Type Methods for Variational Inequality Problems
نویسندگان
چکیده
It is known that the variational inequality problem (VIP) can be converted to a differentiable unconstrained optimization problem via a merit function first considered by Peng and later studied further by Yamashita, Taji and Fukushima. This merit function, called the D-gap function, though is differentiable, is not twice differentiable and its generalized Hessian with existing definitions is very difficult to compute and may not exist in some cases. This paper introduces a computable generalized Hessian (CGH) for the D-gap function in the case that the closed convex set for the VIP is defined by several twice continuously differentiable convex functions. Local superlinear convergence for the generalized Newton method to minimize the D-gap function with the CGH is established. A globally and superlinearly convergent trust region algorithm for the VIP, which utilizes the D-gap function and its CGH, is presented.
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