Continuity of maximal value functionals in normed spaces

被引：0
|
作者：
Jahn J. [1 ]
机构：
[1] Department Mathematik, Universität Erlangen-Nürnberg, Cauerstr. 11, Erlangen
来源：
Applied Set-Valued Analysis and Optimization | 2021年 / 3卷 / 03期
关键词：
Maximal value functional; Necessary optimality condition; Set optimization;
D O I：
10.23952/ASVAO.3.2021.3.06
中图分类号：
O144 [集合论]; O157 [组合数学（组合学）];
学科分类号：
070104 ;
摘要：
This paper examines special maximal value functionals, which are extended support functionals where the objective is linear but the constraint set is nonconvex. In finite-dimensional spaces, it is well-known that these maximal value functionals are continuous. It is shown in the present paper that this result can also be proven in normed spaces without convexity assumptions. As an application, necessary optimality conditions in set optimization are derived. © 2021 Applied Set-Valued Analysis and Optimization.
引用
收藏
页码：317 / 323
页数：6
相关论文
共 50 条
  • [31] Strongly Lacunary Ward Continuity in 2-Normed Spaces
    Cakalli, Huseyin
    Ersan, Sibel
    SCIENTIFIC WORLD JOURNAL, 2014,
  • [32] Continuity of coordinate functionals of filter bases in Banach spaces
    de Rancourt, Noe
    Kania, Tomasz
    Swaczyna, Jaroslaw
    JOURNAL OF FUNCTIONAL ANALYSIS, 2023, 284 (09)
  • [33] CONTINUITY AND BOUNDEDNESS OF LINEAR FUNCTIONALS ON LINEAR RANKED SPACES
    WASHIHARA, M
    PROCEEDINGS OF THE JAPAN ACADEMY, 1967, 43 (07): : 590 - +
  • [34] FUNCTIONALS ON NORMED SEQUENCE SPACES AND UNIFORM EXPONENTIAL INSTABILITY OF EVOLUTION OPERATORS
    Megan, Mihail
    Biris, Larisa
    STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2009, 54 (04): : 81 - 89
  • [35] Bounded 2-linear functionals on the n-normed spaces
    Batkunde, Harmanus
    Rumlawang, Francis Y.
    ASIAN MATHEMATICAL CONFERENCE 2016 (AMC 2016), 2017, 893
  • [36] CONTINUITY OF THE MULTILINEAR MAXIMAL COMMUTATORS IN SOBOLEV SPACES
    Jiang, Xixi
    Liu, Feng
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (03): : 1674 - 1697
  • [37] ON THE CONTINUITY OF DISCRETE MAXIMAL OPERATORS IN SOBOLEV SPACES
    Luiro, Hannes
    Nuutinen, Juho
    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2014, 39 (01) : 175 - 185
  • [38] On Boundary Value Problems in Normed Fuzzy Spaces
    Farajzadeh, Ali
    Hosseinpour, Azadeh
    Kumam, Wiyada
    THAI JOURNAL OF MATHEMATICS, 2022, 20 (01): : 305 - 313
  • [39] WEAK AND NORM CONTINUITY OF SEMIGROUP ACTIONS ON NORMED LINEAR-SPACES
    DZINOTYIWEYI, HAM
    QUARTERLY JOURNAL OF MATHEMATICS, 1982, 33 (129): : 85 - 90
  • [40] SUBMULTIPLICATIVE NONNEGATIVE FUNCTIONALS ON LINEAR MAPS OF LINEAR FINITE DIMENSIONAL NORMED SPACES
    KURZWEIL, J
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 1972, 22 (03) : 454 - &
12345