论文信息 - Structure Preserving Reductions among Convex Optimization Problems

Structure Preserving Reductions among Convex Optimization Problems

Abstract In this paper we introduce the concept of convex optimization problem. Convex optimization problems are studied by giving a formalization of the concept of combinatorial structure, in terms of spectra of approximate solutions, and of reduction which preserves such structure. On this basis a classification of convex NP -optimization problems is introduced and is applied to study the combinatorial structure of several optimization problems associated to well-known NP -complete sets. Conditions on the approximability of such optimization problems are also given and it is shown that structurally isomorphic problems have similar approximability properties.

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