Abstract
Let us consider two sequences of closed convex sets ${A_n}$ and ${B_n}$ converging with respect to the Attouch-Wets convergence to $A$ and $B$, respectively. Given a starting point $a_0$, we consider the sequences of points obtained by projecting onto the ``perturbed'' sets, i.e., the sequences ${a_n}$ and ${b_n}$ defined inductively by $b_n=P_{B_n}(a_{n-1})$ and $a_n=P_{A_n}(b_n)$. \r\n Suppose that $Acap B$ is bounded, we prove that if the couple $(A,B)$ is (boundedly) regular then the couple $(A,B)$ is $d$-stable, i.e., for each ${a_n}$ and ${b_n}$ as above we have $mathrm{dist}(a_n,Acap B) o 0$ and $mathrm{dist}(b_n,Acap B) o 0$. Similar results are obtained also in the case $A cap B=emptyset$, considering the set of best approximation pairs instead of $Acap B$.
Lingua originale | Inglese |
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pagine (da-a) | 521-542 |
Numero di pagine | 22 |
Rivista | Set-Valued and Variational Analysis |
Volume | 30 |
Numero di pubblicazione | 2 |
DOI | |
Stato di pubblicazione | Pubblicato - 2021 |
All Science Journal Classification (ASJC) codes
- Analisi
- Statistica e Probabilità
- Analisi Numerica
- Geometria e Topologia
- Matematica Applicata
Keywords
- Alternating projections method
- Convex feasibility problem
- Regularity
- Set-convergence
- Stability