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We also discuss the applications of the results in robust optimization, especially the robust quadratic matrix inequalities and the robust linear programming models. In the latter application the implementational errors of the solution are taken into account, and the problem is formulated as a semidefinite program.<\/jats:p>","DOI":"10.1137\/s1052623403421498","type":"journal-article","created":{"date-parts":[[2004,7,22]],"date-time":"2004-07-22T21:00:37Z","timestamp":1090530037000},"page":"1140-1162","source":"Crossref","is-referenced-by-count":154,"title":["Multivariate Nonnegative Quadratic Mappings"],"prefix":"10.1137","volume":"14","author":[{"given":"Zhi-Quan","family":"Luo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jos F.","family":"Sturm","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuzhong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,28]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(99)00205-0"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898340299"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"AharonBen\u2010Tal, LaurentEl Ghaoui, ArkadiNemirovski, Robustness, Internat. 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