Geodesic
A method for solving a~general multi-valued complementarity problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 46-53

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We propose an extended version of Chandrasekaran's method for general complementarity problems with multi-valued weakly off-diagonally antitone cost mappings. It allows one either to construct a sequence converging to a solution or to recognize that the problem has no solutions. We also suggest versions of Jacobi's methods for multi-valued inclusions subject to one- and two-sided constraints.
Keywords: complementarity problem, multi-valued mapping, off-diagonal antitonicity, coordinate descent method, multi-valued inclusions. 
@article{IVM_2011_2_a4,
     author = {I. V. Konnov and I. A. Pastukhov},
     title = {A method for solving a~general multi-valued complementarity problem},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {46--53},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_2_a4/}
}
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I. V. Konnov; I. A. Pastukhov. A method for solving a~general multi-valued complementarity problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 46-53. http://geodesic.mathdoc.fr/item/IVM_2011_2_a4/