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Optim."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The final goal of the present paper is computing\/estimating the calmness moduli from below and above of the optimal value function restricted to the set of solvable linear problems. Roughly speaking, these moduli provide measures of the maximum rates of decrease and increase of the optimal value under perturbations of the data (provided that solvability is preserved). This research is developed in the framework of (finite) linear optimization problems under canonical perturbations, i.e., under simultaneous perturbations of the right-hand side (RHS) of the constraints and the coefficients of the objective function. As a first step, part of the work is developed in the context of RHS pertubations only, where a specific formulation for the optimal value function is provided. This formulation constitutes the starting point in obtaining exact formulae\/estimations for the corresponding calmness moduli from below and above. We point out the fact that all expressions for the desired calmness moduli are conceptually tractable (implementable) in so far as they are given exclusively in terms of the nominal data.<\/jats:p>","DOI":"10.1137\/17m112333x","type":"journal-article","created":{"date-parts":[[2018,8,3]],"date-time":"2018-08-03T08:53:27Z","timestamp":1533286407000},"page":"2201-2221","source":"Crossref","is-referenced-by-count":9,"title":["Calmness of the Optimal Value in Linear Programming"],"prefix":"10.1137","volume":"28","author":[{"given":"M. J.","family":"Gisbert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. J.","family":"C\u00e1novas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8864-975X","authenticated-orcid":true,"given":"J.","family":"Parra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F. J.","family":"Toledo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,8,2]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01758841"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:2004013"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"B. Bank, J. Guddat, D. Klatte, B. Kummer, and K. 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