Theory and methods of Euclidian combinatorial optimization: current status and prospects
The paper provides a review of Euclidean combinatorial optimization methods applicable to discrete optimization problems on a set of combinatorial configurations mapped into an arithmetic Euclidean space. Mapping of combinatorial configurations into an arithmetic Euclidean space forms a so called images of combinatorial sets. The paper describes various properties of images and proposes a theory of continuous functional representations and convex extensions for solving this class of problems. The paper concludes with areas of practical application and promising research.
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