LEAST MAJORIZED ELEMENTS AND GENERALIZED POLYMATROIDS

被引：12
|
作者：
TAMIR, A
机构：
来源：
MATHEMATICS OF OPERATIONS RESEARCH | 1995年 / 20卷 / 03期
关键词：
POLYMATROID; MAJORIZATION;
D O I：
10.1287/moor.20.3.583
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 prove that a bounded generalized polymatroid has a least weakly submajorized (supermajorized) vector. Such a vector simultaneously minimizes every nondecreasing (nonincreasing), symmetric and quasi-convex function defined on the generalized polymatroid. The same result herds also for the set of integer vectors of a bounded integral generalized polymatroid. We then extend these results to more general sets, and discuss several computational aspects.
引用
收藏
页码：583 / 589
页数：7
相关论文
共 50 条
  • [1] NESTED MATRICES AND THE EXISTENCE OF LEAST MAJORIZED ELEMENTS
    BAREL, M
    TAMIR, A
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 38 (JUN) : 65 - 72
  • [2] Maximal elements and equilibria for generalized majorized maps
    O'Regan, Donal
    NONLINEAR ANALYSIS-MODELLING AND CONTROL, 2023, 28 (01): : 116 - 132
  • [3] MAXIMAL ELEMENTS OF fC,θ-MAJORIZED MAPPINGS AND APPLICATIONS TO GENERALIZED GAMES
    Du, Y. M.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2014, 40 (05) : 1153 - 1167
  • [4] Characterizing and recognizing generalized polymatroids
    András Frank
    Tamás Király
    Júlia Pap
    David Pritchard
    Mathematical Programming, 2014, 146 : 245 - 273
  • [5] Generalized polymatroids and submodular flows
    Frank, Andras
    Tardos, Eva
    Mathematical Programming, Series B, 1988, 42 (01): : 489 - 563
  • [6] Characterizing and recognizing generalized polymatroids
    Frank, Andras
    Kiraly, Tamas
    Pap, Julia
    Pritchard, David
    MATHEMATICAL PROGRAMMING, 2014, 146 (1-2) : 245 - 273
  • [7] GENERALIZED POLYMATROIDS AND SUBMODULAR FLOWS
    FRANK, A
    TARDOS, E
    MATHEMATICAL PROGRAMMING, 1988, 42 (03) : 489 - 563
  • [8] STICKY POLYMATROIDS ON AT MOST FIVE ELEMENTS
    Csirmaz, Laszlo
    STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2021, 58 (01) : 136 - 146
  • [9] Generalized Index Coding Problem and Discrete Polymatroids
    Thomas, Anoop
    Rajan, B. Sundar
    ENTROPY, 2020, 22 (06)
  • [10] Generalized Index Coding Problem and Discrete Polymatroids
    Thomas, Anoop
    Rajan, B. Sundar
    2017 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2017, : 2553 - 2557
12345