{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article9217","name":"Surrogate Optimization for p-Norms","abstract":"In this paper, we study the effect of surrogate objective functions in optimization problems. We introduce surrogate ratio as a measure of such effect, where the surrogate ratio is the ratio between the optimal values of the original and surrogate objective functions.\r\n\r\nWe prove that the surrogate ratio is at most mu^{|1\/p - 1\/q|} when the objective functions are p- and q-norms, and the feasible region is a mu-dimensional space (i.e., a subspace of R^mu), a mu-intersection of matroids, or a mu-extendible system. We also show that this is the best possible bound. In addition, for mu-systems, we demonstrate that the ratio becomes mu^{1\/p} when p < q and unbounded if p > q. Here, a mu-system is an independence system such that for any subset of ground set the ratio of the cardinality of the largest to the smallest maximal independent subset of it is at most mu. We further extend our results to the surrogate ratios for approximate solutions.","keywords":["surrogate optimization","matroid","extendible system","p-norm"],"author":[{"@type":"Person","name":"Kawase, Yasushi","givenName":"Yasushi","familyName":"Kawase"},{"@type":"Person","name":"Makino, Kazuhisa","givenName":"Kazuhisa","familyName":"Makino"}],"position":41,"pageStart":"41:1","pageEnd":"41:13","dateCreated":"2016-12-07","datePublished":"2016-12-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kawase, Yasushi","givenName":"Yasushi","familyName":"Kawase"},{"@type":"Person","name":"Makino, Kazuhisa","givenName":"Kazuhisa","familyName":"Makino"}],"copyrightYear":"2016","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ISAAC.2016.41","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6267","volumeNumber":64,"name":"27th International Symposium on Algorithms and Computation (ISAAC 2016)","dateCreated":"2016-12-07","datePublished":"2016-12-07","editor":{"@type":"Person","name":"Hong, Seok-Hee","givenName":"Seok-Hee","familyName":"Hong"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article9217","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6267"}}}