- Title
- Stability of the lower level sets of ICAR functions
- Creator
- López, Marco; Rubinov, Alex; Vera De Serio, Virginia
- Date
- 2005
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/70111
- Identifier
- vital:530
- Identifier
-
https://doi.org/10.1081/NFA-200052008
- Identifier
- ISSN:0163-0563
- Abstract
- In this paper, we study the stability of the lower level set {x E R++n | f (x) ≤ 0} of a finite valued increasing convex-along-rays (ICAR) function f defined on R++n. In monotonic analysis, ICAR functions play the role of usual convex functions in classical convex analysis. We show that each ICAR function f is locally Lipschitz on int dom f and that the pointwise convergence of a sequence of ICAR functions implies its uniform convergence on each compact subset of R ++n. The latter allows us to establish stability results for ICAR functions in some sense similar to those for convex functions. Copyright © Taylor & Francis, Inc.; C1
- Publisher
- Taylor & Francis
- Relation
- Numerical Functional Analysis and Optimization Vol. 26, no. 1 (2005), p. 113-127
- Rights
- Copyright Taylor & Francis
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; Increasing convex-along-rays functions; Solution set mapping; Stability; Convergence of numerical methods; Parameter estimation; Set theory; Vectors; Convex functions; Parameter space; Functions
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