{"title":"Second-order conditions for non-uniformly convex integrands: quadratic\n growth in $L^1$","authors":"D. Wachsmuth, G. Wachsmuth","doi":"10.46298/jnsao-2022-8733","DOIUrl":null,"url":null,"abstract":"We study no-gap second-order optimality conditions for a non-uniformly convex\nand non-smooth integral functional. The integral functional is extended to the\nspace of measures. The obtained second-order derivatives contain integrals on\nlower-dimensional manifolds. The proofs utilize the convex pre-conjugate, which\nis an integral functional on the space of continuous functions. Applications to\nnon-smooth optimal control problems are given.","PeriodicalId":250939,"journal":{"name":"Journal of Nonsmooth Analysis and Optimization","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonsmooth Analysis and Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/jnsao-2022-8733","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
We study no-gap second-order optimality conditions for a non-uniformly convex
and non-smooth integral functional. The integral functional is extended to the
space of measures. The obtained second-order derivatives contain integrals on
lower-dimensional manifolds. The proofs utilize the convex pre-conjugate, which
is an integral functional on the space of continuous functions. Applications to
non-smooth optimal control problems are given.
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