{"title":"Higher-Order Optimality Conditions in Set-Valued Optimization with Respect to General Preference Mappings.","authors":"Anna Michalak, Marcin Studniarski","doi":"10.1007/s11228-022-00627-2","DOIUrl":null,"url":null,"abstract":"<p><p>We present higher order necessary conditions for a model of welfare economics, where the preference mapping has a star-shape property. We assume that the preferences can be satiable and can be described by an arbitrary preference set, without the use of utility functions. These conditions are formulated in terms of higher-order directional derivatives of multivalued mappings, and the variable domination structure is not given by cones.</p>","PeriodicalId":49537,"journal":{"name":"Set-Valued and Variational Analysis","volume":"30 3","pages":"975-993"},"PeriodicalIF":1.3000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8768435/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Set-Valued and Variational Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11228-022-00627-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/1/19 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
We present higher order necessary conditions for a model of welfare economics, where the preference mapping has a star-shape property. We assume that the preferences can be satiable and can be described by an arbitrary preference set, without the use of utility functions. These conditions are formulated in terms of higher-order directional derivatives of multivalued mappings, and the variable domination structure is not given by cones.
期刊介绍：
The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.
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