On the Extension of Continuous Quasiconvex Functions

被引：2
|
作者：
De Bernardi, Carlo Alberto [1 ]
机构：
[1] Univ Cattolica Sacro Cuore, Dipartimento Matemat Sci Econ Finanziarie & Attua, Via Necchi 9, I-20123 Milan, Italy
来源：
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2020年 / 187卷 / 02期
关键词：
Quasiconvex function; Extension; Convex set; Normed linear space; POLYHEDRAL SECTIONS; DIFFERENTIABILITY; POINTS;
D O I：
10.1007/s10957-020-01767-x
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
We study the problem of extending continuous quasiconvex real-valued functions from a subspace of a real normed linear space. Our results are essentially finite-dimensional and are based on a technical lemma which permits to "extend" a nested family of open convex subsets of a given subspace to a nested family of open convex sets in the whole space, in such a way that certain topological conditions are satisfied.
引用
收藏
页码：421 / 430
页数：10
相关论文
共 50 条
  • [1] On the Extension of Continuous Quasiconvex Functions
    Carlo Alberto De Bernardi
    [J]. Journal of Optimization Theory and Applications, 2020, 187 : 421 - 430
  • [2] ON EXTENSION OF UNIFORMLY CONTINUOUS QUASICONVEX FUNCTIONS
    de Bernardi, Carlo Alberto
    Vesely, Libor
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, : 1705 - 1716
  • [3] Extendability of continuous quasiconvex functions from subspaces
    Bernardi, Carlo Alberto De
    Vesely, Libor
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 526 (02)
  • [4] Approximation of quasiconvex functions by neatly quasiconvex functions
    Suliman Al-Homidan
    Loai Shaalan
    [J]. Optimization Letters, 2021, 15 : 979 - 989
  • [5] Approximation of quasiconvex functions by neatly quasiconvex functions
    Al-Homidan, Suliman
    Shaalan, Loai
    [J]. OPTIMIZATION LETTERS, 2021, 15 (03) : 979 - 989
  • [6] On the extension of continuous functions
    de Groot, J
    [J]. PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN, 1942, 45 (6/10): : 842 - 843
  • [7] ON ω-QUASICONVEX FUNCTIONS
    Tabor, Jacek
    Tabor, Jozef
    Zoldak, Marek
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2012, 15 (04): : 845 - 857
  • [8] Quasiconvex functions can be approximated by quasiconvex polynomials
    Heinz, Sebastian
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2008, 14 (04) : 795 - 801
  • [9] EXTENSION OF CONTINUOUS FUNCTIONS IN BETAD
    NEGREPON.S
    [J]. PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1968, 71 (04): : 393 - &
  • [10] CONTINUOUS LINEAR EXTENSION OF FUNCTIONS
    Koyama, A.
    Stasyuk, I.
    Tymchatyn, E. D.
    Zagorodnyuk, A.
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (11) : 4149 - 4155
12345