Geodesic
Two-level iterative method for non-stationary mixed variational inequalities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 50-61

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We consider a mixed variational inequality problem involving a set-valued non-monotone mapping and a general convex function, where only approximation sequences are known instead of exact values of the cost mapping and function, and feasible set. We suggest to apply a two-level approach with inexact solutions of each particular problem with a descent method and partial penalization and evaluation of accuracy with the help of a gap function. Its convergence is attained without concordance of penalty, accuracy, and approximation parameters under coercivity type conditions.
Keywords: mixed variational inequality, non-stationarity, non-monotone mappings, potential mappings, approximate solutions, penalty method, gap function. 
@article{IVM_2017_10_a5,
     author = {I. V. Konnov and Salahuddin},
     title = {Two-level iterative method for non-stationary mixed variational inequalities},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {50--61},
     publisher = {mathdoc},
     number = {10},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_10_a5/}
}
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I. V. Konnov; Salahuddin. Two-level iterative method for non-stationary mixed variational inequalities. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 50-61. http://geodesic.mathdoc.fr/item/IVM_2017_10_a5/