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An Equivalence Theorem to Integrate Entropy‐Maximizing Submodels within Overall Mathematical‐Programming Frameworks
Author(s) -
Coelho J. D.,
Wilson A. G.
Publication year - 1977
Publication title -
geographical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 65
eISSN - 1538-4632
pISSN - 0016-7363
DOI - 10.1111/j.1538-4632.1977.tb00569.x
Subject(s) - equivalence (formal languages) , mathematical optimization , computer science , lemma (botany) , minification , entropy (arrow of time) , mathematics , discrete mathematics , ecology , physics , poaceae , quantum mechanics , biology
This paper presents a lemma and a theorem which demonstrate equivalent ways of formulating certain mathematical‐programming problems. The first shows, in general terms, how constraints can be “absorbed” into the objective function and vice versa. The second shows how such ideas can be applied to spatial analysis problems involving the minimization of development costs subject to interactions being determined by (suboptimal) entropy‐maximizing models. This provides both a new perspective on the relationship between programming and entropy models, and formulations that are computationally convenient.