- Title
- Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings : decoupling approach revisited
- Creator
- Fabian, Marian; Kruger, Alexander; Mehlitz, Patrick
- Date
- 2024
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/198876
- Identifier
- vital:19106
- Identifier
-
https://doi.org/10.1016/j.jmaa.2023.127985
- Identifier
- ISSN:0022-247X (ISSN)
- Abstract
- We revisit the decoupling approach widely used (often intuitively) in nonlinear analysis and optimization and initially formalized about a quarter of a century ago by Borwein & Zhu, Borwein & Ioffe and Lassonde. It allows one to streamline proofs of necessary optimality conditions and calculus relations, unify and simplify the respective statements, clarify and in many cases weaken the assumptions. In this paper we study weaker concepts of quasiuniform infimum, quasiuniform lower semicontinuity and quasiuniform minimum, putting them into the context of the general theory developed by the aforementioned authors. Along the way, we unify the terminology and notation and fill in some gaps in the general theory. We establish rather general primal and dual necessary conditions characterizing quasiuniform
- Publisher
- Academic Press Inc.
- Relation
- Journal of Mathematical Analysis and Applications Vol. 532, no. 2 (2024), p.; https://purl.org/au-research/grants/arc/DP160100854
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- http://creativecommons.org/licenses/by/4.0/
- Rights
- Copyright © 2023 The Author(s)
- Rights
- Open Access
- Subject
- 4901 Applied mathematics; 4903 Numerical and computational mathematics; 4904 Pure mathematics; Calculus; Fuzzy multiplier rule; Fuzzy sum rule; Non-Lipschitz optimization; Variational analysis
- Full Text
- Reviewed
- Funder
- Research is supported by the Australian Research Council , project DP160100854 ; the DFG Grant Bilevel Optimal Control: Theory, Algorithms, and Applications, grant WA 3636/4-2 , within the Priority Program SPP 1962 (Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation and Hierarchical Optimization); and grants GA
- Hits: 1022
- Visitors: 1025
- Downloads: 7
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Published version | 832 KB | Adobe Acrobat PDF | View Details Download |