Ann Oper Res https://doi.org/10.1007/s10479-017-2709-7 S.I.:OR IN TRANSPORTATION Pointwise and global well-posedness in set optimization: a direct approach Giovanni P. Crespi 1 · Mansi Dhingra 2 · C. S. Lalitha 3 © Springer Science+Business Media, LLC, part of Springer Nature 2017 Abstract The aim of this paper is to characterize some of the pointwise and global well- posedness notions available in literature for a set optimization problem completely by compactness or upper continuity of an appropriate minimal solution set maps. The char- acterizations of compactness of set-valued maps, lead directly to many characterizations for well-posedness. Sufficient conditions are also given for global well-posedness. Keywords Well-posedness · Set optimization · l -minimal solution · Compactness · Upper continuity 1 Introduction Optimization problems with set-valued objectives appear in many areas for instance, bilevel optimization, fuzzy optimization, interval optimization, game theory and mathematical eco- nomics. For some motivating examples one may refer to the book by Khan et al. (2015). A fast growing approach, known as set-optimization, was initiated by Kuroiwa (1999), Kuroiwa (2001), who proposed order relations among sets to define minimality notions accordingly. Among other topics, well-posedness plays a significant role in the study of sta- B C. S. Lalitha cslalitha@maths.du.ac.in; cslalitha1@gmail.com Giovanni P. Crespi giovanni.crespi@uninsubria.it Mansi Dhingra mansidhingra7@gmail.com 1 Department of Economics, Università degli Studi dell’Insubria, via Monte Generoso, 71, 21100 Varese, Italy 2 Department of Mathematics, University of Delhi, Delhi 110007, India 3 Department of Mathematics, University of Delhi, South Campus, Benito Jaurez Road, New Delhi 110021, India 123