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We introduce and study certain classes of optimization problems over the real numbers. The classes are defined by logical means, relying on metafinite model theory for so called R-structures (see [11], [10]). More precisely, based on a real analogue of Fagin's theorem [11] we deal with two classes MAX-N P R and MIN-N P R of maximization and minimization… (More)

A fundamental research area in relation with analyzing the complexity of optimization problems are approximation algorithms. For combinatorial optimization a vast theory of approximation algorithms has been developed, see [1]. Many natural optimization problems involve real numbers and thus an uncountable search space of feasible solutions. A uniform… (More)

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