A projection algorithm for non-monotone variational inequalities
| Autor: | Regina S. Burachik, R. Díaz Millán |
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| Přispěvatelé: | Burachik, Regina S, Millán, R Díaz |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Numerical Analysis 021103 operations research outer-semicontinuous operator Applied Mathematics 0211 other engineering and technologies Solution set Monotonic function 010103 numerical & computational mathematics 02 engineering and technology variational inequality inner-semicontinuous operator 01 natural sciences Dual (category theory) projection algorithms Operator (computer programming) Iterated function Convergence (routing) Variational inequality Applied mathematics Geometry and Topology 0101 mathematics Analysis Dykstra's projection algorithm Mathematics |
| Popis: | We introduce a projection-type algorithm for solving the variational inequality problem for point-to-set operators, and establish its convergence properties. Namely, we assume that the operator of the variational inequality is continuous in the point-to-set sense, i.e., inner- and outer-semicontinuous. Under the assumption that the dual solution set is not empty, we prove that our method converges to a solution of the variational inequality. Instead of the monotonicity assumption, we require the non-emptiness of the solution set of the dual formulation of the variational inequality. We provide numerical experiments illustrating the behaviour of our iterates. Moreover, we compare our new method with a recent similar one. Refereed/Peer-reviewed |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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