Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems
We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the...
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| Published in: | Journal of mathematical analysis and applications Vol. 435; no. 2; pp. 1688 - 1700 |
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| Language: | English |
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15.03.2016
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| ISSN: | 0022-247X, 1096-0813 |
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| Abstract | We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the celebrated Opial Lemma we prove weak ergodic convergence of the orbits to a solution of the constrained variational inequality under investigation. If one of the operators involved satisfies stronger monotonicity properties, then strong convergence of the trajectories can be shown. |
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| AbstractList | We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on Lyapunov analysis and on the ergodic continuous version of the celebrated Opial Lemma we prove weak ergodic convergence of the orbits to a solution of the constrained variational inequality under investigation. If one of the operators involved satisfies stronger monotonicity properties, then strong convergence of the trajectories can be shown. |
| Author | Boţ, Radu Ioan Csetnek, Ernö Robert |
| Author_xml | – sequence: 1 givenname: Radu Ioan orcidid: 0000-0002-4469-314X surname: Boţ fullname: Boţ, Radu Ioan email: radu.bot@univie.ac.at – sequence: 2 givenname: Ernö Robert surname: Csetnek fullname: Csetnek, Ernö Robert email: ernoe.robert.csetnek@univie.ac.at |
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| Cites_doi | 10.1007/s10013-013-0050-2 10.1007/s10957-013-0414-5 10.1007/s10957-014-0700-x 10.1023/B:JOTA.0000005445.21095.02 10.1007/978-1-4419-9467-7 10.1137/100789464 10.1080/02331934.2014.971412 10.1007/s10957-011-9936-x 10.1007/s11228-008-0093-9 10.1137/110820300 10.1137/100784114 10.1016/j.jde.2009.06.014 10.1023/A:1020639314056 10.1007/s11228-014-0274-7 10.1007/s10957-013-0296-6 |
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| Keywords | Lyapunov analysis Penalty schemes Monotone inclusions Dynamical systems Forward–backward algorithm |
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| SubjectTerms | Dynamical systems Forward–backward algorithm Lyapunov analysis Monotone inclusions Penalty schemes |
| Title | Approaching the solving of constrained variational inequalities via penalty term-based dynamical systems |
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