Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems

Qamrul Hasan Ansari () and Pradeep Kumar Sharma ()
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Qamrul Hasan Ansari: Aligarh Muslim University
Pradeep Kumar Sharma: University of Delhi South Campus

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 13, 247-279

Abstract: Abstract In this paper, we study several interesting basic properties of generalized oriented distance function with respect to co-radiant sets or free disposal sets, which are more general than a cone and play an important role to study quasi-minimal solutions of set optimization problems. In particular, we deal with some special properties, namely, translation property, subadditivity and monotonicity, by using co-radiant sets. Moreover, we investigate several kinds of monotonicity properties by means of nonconvex free disposal sets. As an application, we study some optimality conditions for quasi-minimal solutions of set optimization problems by using generalized oriented distance function. At the end, we give an existence theorem for cone saddle-point for set-valued maps. Several examples are given to verify the validity and effectiveness of the derived results.

Keywords: Oriented distance function; Set relations; Set optimization; Quasi-minimal solutions; Co-radiant set; Free disposal set; 49J53; 90C29; 90C30 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-022-02024-z

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