Geodesic
Descent method with inexact linesearch procedure for mixed variational inequalities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2009), pp. 37-44

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We propose a descent method with respect to a merit function for a mixed variational inequality, involving a general nonlinear mapping and a convex but not necessarily differentiable function. The method utilizes an inexact linesearch procedure. Its convergence is proved under the additional assumptions of continuity and strong monotonicity of the cost mapping.
Keywords: mixed variational inequalities, descent method, inexact linesearch. 
@article{IVM_2009_8_a4,
     author = {I. V. Konnov},
     title = {Descent method with inexact linesearch procedure for mixed variational inequalities},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {37--44},
     publisher = {mathdoc},
     number = {8},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_8_a4/}
}
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%F IVM_2009_8_a4
I. V. Konnov. Descent method with inexact linesearch procedure for mixed variational inequalities. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2009), pp. 37-44. http://geodesic.mathdoc.fr/item/IVM_2009_8_a4/