On radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups

We extend some recent results on radiant and normal sets in , increasing positively homogeneous and increasing co-radiant functions plus-radiant and downward sets in , topical and sub-topical functions to the unifying framework of subsets of A n and functions f:A n → where A=(A,≤, ⊗ ) is a condition...

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Bibliographic Details
Published inOptimization Vol. 53; no. 4; pp. 393 - 428
Main Author Singer, Ivan
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.08.2004
Taylor & Francis LLC
Subjects
Abstract convexity
Continuous lattice
Downward set
Lattice ordered group
Mathematical models
Mathematics Subject Classification 2000: Primary: 26B25
Optimization
Radiant set
Secondary: 49N15
Studies
Sub-topical function
Topical function
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ISSN0233-1934
1029-4945
DOI10.1080/02331930412331282418

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Summary:We extend some recent results on radiant and normal sets in , increasing positively homogeneous and increasing co-radiant functions plus-radiant and downward sets in , topical and sub-topical functions to the unifying framework of subsets of A n and functions f:A n → where A=(A,≤, ⊗ ) is a conditionally complete lattice ordered group and is the minimal enlargement of A. For results involving closedness, continuity and semi-continuity, we assume that the lattice A is continuous and we use the order topology on A n and A.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331930412331282418