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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| Published in | Optimization Vol. 53; no. 4; pp. 393 - 428 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis Group
01.08.2004
Taylor & Francis LLC |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0233-1934 1029-4945 |
| DOI | 10.1080/02331930412331282418 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. Recent results are extended on radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups. For results involving closedness, continuity and semi-continuity, assume that the lattice A is continuous and use the order topology on An and A. |
| Author | Singer †, Ivan |
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| Cites_doi | 10.1023/A:1009710513565 10.1080/02331930310001637396 10.1080/0233193021000004949 10.1090/S0002-9947-99-02153-4 10.1080/02331939408843993 10.1007/978-1-4757-3200-9 10.1023/A:1015583411806 10.1080/02331930108844567 10.1017/CBO9780511662508 |
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| References | Gunawardena J (bib6) 1995 Birkhoff G (bib3) 1967; 25 Bourbaki N (bib4) 1942 bib14 Kolokoltsov VN (bib7) 1997 bib10 Rubinov AM (bib13) 2000 Zimmermann K (bib17) 1979; 17 bib9 bib8 bib5 Singer I (bib15) 1997 bib16 bib1 bib2 Moreau J-J (bib11) 1970; 49 Rubinov AM (bib12) 1998; 32 |
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| Snippet | We extend some recent results on radiant and normal sets in
, increasing positively homogeneous and increasing co-radiant functions
plus-radiant and downward... Recent results are extended on radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups. For results involving... |
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| SubjectTerms | 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 |
| Title | On radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups |
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