1. Existence and Asymptotic Behavior of Second-Order Difference Equation with Tikhonov Regularization.
- Author
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Balhag, Aicha, Chbani, Zaki, and Riahi, Hassan
- Subjects
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TIKHONOV regularization , *ASYMPTOTIC theory in partial differential equations , *DIFFERENCE equations , *MONOTONE operators , *HILBERT space , *STOCHASTIC convergence , *CONVEX domains - Abstract
We study existence and asymptotic behavior of a bounded solution of the following Tikhonov regularized second-order difference equation (): where, A is a multivalued maximal monotone operator defined on a Hilbert space and are positive real parameters. We first prove under condition existence of unique bounded solution of (). For asymptotic behavior, we use a suitable assumption on cn and to prove strong convergence of un to the element of minimal norm of Some applications are thereafter discussed with respect to minimization and saddle-point problems. Specially, we study the rate of convergence of optimal values in convex minimization and convex-concave problems. We end the paper by concluding remarks and noticing some research perspectives. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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