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

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  • Qamrul Hasan Ansari

    (Aligarh Muslim University)

  • Pradeep Kumar Sharma

    (University of Delhi South Campus)

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.

Suggested Citation

  • Qamrul Hasan Ansari & Pradeep Kumar Sharma, 2022. "Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 247-279, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-022-02024-z
    DOI: 10.1007/s10957-022-02024-z
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