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

DOI10.1080/02331930412331282418zbMath1066.26006OpenAlexW2079732329MaRDI QIDQ4820400

Ivan Singer

Publication date: 15 October 2004

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930412331282418

zbMATH Keywords

radiant setabstract convexitytopical functionsub-topical functionlattice ordered groupdownward set

Mathematics Subject Classification ID

Convexity of real functions of several variables, generalizations (26B25) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20)

Related Items (9)

Global optimization of the difference of two increasing plus-convex-along-rays functions ⋮ Some results on abstract convexity of functions ⋮ Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions ⋮ Extended-valued topical and anti-topical functions on semimodules. ⋮ Characterizing global maximizers of the difference of sub-topical functions ⋮ Characterizations of minimal elements of topical functions on semimodules with applications ⋮ Topical functions on semimodules and generalizations ⋮ Max-plus convex sets and max-plus semispaces. II ⋮ Unnamed Item

Cites Work

• On conjugations for functions with values in extensions of ordered groups
• Downward sets and their separation and approximation properties
• Further Applications of the Additive Min-type Coupling Function
• Densities of idempotent measures and large deviations
• Topologies on lattice ordered groups, separation from closed downward sets and conjugations of type Lau
• Topical and sub-topical functions, downward sets and abstract convexity
• Dualities
• Abstract convexity and global optimization

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