Geodesic
A partial regularization method for a generalized primal-dual system of inequalities
Numerical methods and programming, Tome 11 (2010) no. 4, pp. 318-325.

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A generalized primal-dual system is considered. The problem is reformulated as an equivalent variational inequality whose main mapping does not possess a monotonicity property and is not the gradient mapping of any function. In order to solve the problem, a partial regularization method is proposed. Its convergence is proved under certain coercitivity-type conditions. An application to an economic equilibrium problem is discussed. The work was supported by the Russian Foundation for Basic Research (project 10-01-00629).
Keywords: generalized primal-dual system; nonmonotone variational inequality; partial regularization method; sufficient convergence conditions. 
@article{VMP_2010_11_4_a2,
     author = {D. A. Dyabilkin and I. V. Konnov},
     title = {A partial regularization method for a generalized primal-dual system of inequalities},
     journal = {Numerical methods and programming},
     pages = {318--325},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2010_11_4_a2/}
}
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D. A. Dyabilkin; I. V. Konnov. A partial regularization method for a generalized primal-dual system of inequalities. Numerical methods and programming, Tome 11 (2010) no. 4, pp. 318-325. http://geodesic.mathdoc.fr/item/VMP_2010_11_4_a2/