Back to Search
Start Over
Regularity and Stability for a Convex Feasibility Problem
- Source :
- Set-Valued and Variational Analysis. 30:521-542
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
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 on the "perturbed" sets, i.e., the sequences $\{a_n\}$ and $\{b_n\}$ defined inductively by $b_n=P_{B_n}(a_{n-1})$ and $a_n=P_{A_n}(b_n)$. Suppose that $A\cap B$ (or a suitable substitute if $A \cap B=\emptyset$) 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 $\mathrm{dist}(a_n,A\cap B)\to 0$ and $\mathrm{dist}(b_n,A\cap B)\to 0$.<br />Comment: 16 pages. arXiv admin note: text overlap with arXiv:1907.13402
- Subjects :
- 47J25, 90C25, 90C48
Statistics and Probability
Numerical Analysis
Applied Mathematics
Convex feasibility problem
Stability (learning theory)
Regular polygon
Settore SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE
Settore MAT/05 - ANALISI MATEMATICA
Regularity
Combinatorics
Mathematics::Group Theory
Optimization and Control (math.OC)
Bounded function
Convergence (routing)
FOS: Mathematics
Point (geometry)
Geometry and Topology
Alternating projections method
Mathematics::Representation Theory
Set-convergence
Mathematics - Optimization and Control
Stability
Analysis
Mathematics
Subjects
Details
- ISSN :
- 18770541 and 18770533
- Volume :
- 30
- Database :
- OpenAIRE
- Journal :
- Set-Valued and Variational Analysis
- Accession number :
- edsair.doi.dedup.....8671c05c40501e7251d55a603b959959