Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: Decoupling approach revisited

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00580563" target="_blank" >RIV/67985840:_____/24:00580563 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2023.127985" target="_blank" >https://doi.org/10.1016/j.jmaa.2023.127985</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2023.127985" target="_blank" >10.1016/j.jmaa.2023.127985</a>

Result language
angličtina
Original language name
Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: Decoupling approach revisited
Original language description
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 epsilon-minima of the sum of two functions. The obtained fuzzy multiplier rules are formulated in general Banach spaces in terms of Clarke subdifferentials and in Asplund spaces in terms of Frechet subdifferentials. The mentioned fuzzy multiplier rules naturally lead to certain fuzzy subdifferential calculus results. An application from sparse optimal control illustrates applicability of the obtained findings.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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