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Disjunctive optimization, max-separable problems and extremal algebras

✍ Scribed by Karel Zimmermann


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
127 KB
Volume
293
Category
Article
ISSN
0304-3975

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✦ Synopsis


The paper was motivated by solution methods suggested in the literature for solving linear optimization problems over (max; +)-or (max; min)-algebras and certain class of so called max-separable optimization problems. General features of these optimization problems, which play a crucial role in the optimization methods were used to formulate a general class of optimization problems with disjunctive constraints and a max-separable objective function and suggest a solution procedure for solving such problems. Linear problems over (max; +)-algebras and the max-separable problems are contained in this general class of optimization problems as special cases.


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Three classes of finite structures are related by extremal properties: complete d-partite d-uniform hypergraphs, d-dimensional affine cubes of integers, and families of 2 d sets forming a d-dimensional Boolean algebra. We review extremal results for each of these classes and derive new ones for Bool