Journal of Global Optimization

, Volume 73, Issue 2, pp 447–463 | Cite as

Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior

  • Meenakshi GuptaEmail author
  • Manjari Srivastava


In this paper, we introduce three types of well-posedness for a set optimization problem (u-SOP). Some necessary and sufficient conditions for these well-posedness have been established. Two different scalar optimization problems involving a generalized oriented distance function have been considered. Characterization of u-minimal solutions of (u-SOP) in terms of solutions of these scalar optimization problems have been obtained. Finally, equivalence of well-posedness of (u-SOP) with well-posedness of these scalar optimization problems have been established.


Set optimization Well-posedness Hausdorff set-convergence Nonlinear scalarization function 

Mathematics Subject Classification

49J53 49K40 90C48 


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DelhiNew DelhiIndia
  2. 2.Department of Mathematics, Miranda HouseUniversity of DelhiNew DelhiIndia

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