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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 52, 2003 - Issue 6
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Original Articles

Topologies on lattice ordered groups, separation from closed downward sets and conjugations of type Lau

Marianne Akian* INRIA, Domaine de Voluceau, 78153 Le Chesnay Cédex, FranceView further author information
&
Ivan Singer Institute of Mathematics, P.O. Box 1-764, RO-70700 Bucharest, Romania
Pages 629-672 | Received 28 Mar 2003, Accepted 01 Oct 2003, Published online: 13 May 2010

Citations (15)

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Read on this site (3)

H. Barsam & H. Mohebi. (2016) Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions. Numerical Functional Analysis and Optimization 37:11, pages 1354-1377.
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Nicolae Popovici . (2005) Pareto reducible multicriteria optimization problems. Optimization 54:3, pages 253-263.
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Ivan Singer . (2004) On radiant sets, downward sets, topical functions and sub-topical functions in lattice ordered groups. Optimization 53:4, pages 393-428.
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Articles from other publishers (12)

Paul Poncet. (2022) Transporting continuity properties from a poset to its subposets. Theoretical Computer Science 912, pages 109-132.
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Sara Hassani & Hossein Mohebi. (2017) Characterizations of minimal elements of topical functions on semimodules with applications. Linear Algebra and its Applications 520, pages 104-124.
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Ivan Singer & Viorel Nitica. (2014) Extended-valued topical and anti-topical functions on semimodules. Linear Algebra and its Applications 446, pages 25-70.
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Paul Poncet. (2013) How regular can maxitive measures be?. Topology and its Applications 160:4, pages 606-619.
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Marianne Akian, Stéphane Gaubert, Viorel Niţică & Ivan Singer. (2011) Best approximation in max-plus semimodules. Linear Algebra and its Applications 435:12, pages 3261-3296.
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Paul Poncet. (2011) A decomposition theorem for maxitive measures. Linear Algebra and its Applications 435:7, pages 1672-1680.
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Ivan Singer. (2010) Elementary topical functions on b-complete semimodules over b-complete idempotent semifields. Linear Algebra and its Applications 433:11-12, pages 2139-2146.
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Stéphane Gaubert & Ricardo D. Katz. (2009) The tropical analogue of polar cones. Linear Algebra and its Applications 431:5-7, pages 608-625.
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Stéphane Gaubert & Ricardo D. Katz. (2007) The Minkowski theorem for max-plus convex sets. Linear Algebra and its Applications 421:2-3, pages 356-369.
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Mohamed Ait Mansour, Nicolae Popovici & Michel Théra. (2006) On Directed Sets and their Suprema. Positivity 11:1, pages 155-169.
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M. Ait Mansour, A. Metrane & M. Théra. (2006) Lower Semicontinuous Regularization for Vector-Valued Mappings. Journal of Global Optimization 35:2, pages 283-309.
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Jean-Paul Penot. 2006. Generalized Convexity and Related Topics. Generalized Convexity and Related Topics 399 414 .

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