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We establish a new characterization of tilt-stable local minimizers for a broad class of unconstrained optimization problems in terms of a uniform positive-definiteness of the subgradient graphical derivative of the objective function around the point in question. By applying this result to nonlinear programming under the metric subregularity constraint qualification, we derive second-order characterizations and several new sufficient conditions for tilt stability. In particular, we show that each stationary point of a nonlinear programming problem satisfying the metric subregularity constraint qualification is a tilt-stable local minimizer if the classical strong second-order sufficient condition holds.<\/jats:p>","DOI":"10.1137\/17m1130794","type":"journal-article","created":{"date-parts":[[2018,8,16]],"date-time":"2018-08-16T11:05:50Z","timestamp":1534417550000},"page":"2246-2273","source":"Crossref","is-referenced-by-count":18,"title":["Characterization of Tilt Stability via Subgradient Graphical Derivative with Applications to Nonlinear Programming"],"prefix":"10.1137","volume":"28","author":[{"given":"Nguyen Huy","family":"Chieu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Le Van","family":"Hien","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tran T. 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