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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-22230L" target="_blank" >GF20-22230L: Banachovy prostory spojitých a lipschitzovských funkcí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

532

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

39

Strana od-do

127985

Kód UT WoS článku

001128354400001

EID výsledku v databázi Scopus

2-s2.0-85182213029