Some properties of generalized oriented distance function and their applications to set optimization problems

Ansari, Qamrul Hasan and Sharma, Pradeep Kumar (2022) Some properties of generalized oriented distance function and their applications to set optimization problems. Journal of Optimization Theory and Applications, 193 (1-3), 247-279. (doi:10.1007/s10957-022-02024-z).

Record type: Article

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.

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More information

Accepted/In Press date: 4 March 2022

e-pub ahead of print date: 31 March 2022

Published date: June 2022

Additional Information: Funding Information: The authors are grateful to the handling editor and two anonymous referees for their valuable comments and suggestions, which helped to improve the previous draft of the paper. In this research, the first author was supported by DST-SERB Project No. MTR/2017/000135, while second author was supported by UGC-Dr. D.S. Kothari Post Doctoral Fellowship No. F.4-2/2006 (BSR)/MA/19-20/0040.

Keywords: Co-radiant set, Free disposal set, Oriented distance function, Quasi-minimal solutions, Set optimization, Set relations