Characterization of Norm-Based Robust Solutions in Vector Optimization

Morteza Rahimi () and Majid Soleimani-damaneh ()
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Morteza Rahimi: University of Tehran
Majid Soleimani-damaneh: University of Tehran

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 13, 554-573

Abstract: Abstract In this paper, we study the norm-based robust (efficient) solutions of a vector optimization problem. We define two kinds of non-ascent directions in terms of Clarke’s generalized gradient and characterize norm-based robustness by means of the newly defined directions. This is done under a basic constraint qualification. We extend the provided characterization to vector optimization problems with conic constraints and semi-infinite ones. Moreover, we derive a necessary condition for norm-based robustness utilizing a non-smooth gap function.

Keywords: Vector optimization; Non-smooth optimization; Robust optimization; Clarke’s generalized gradient.; 90C29; 90C31; 49J52 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-020-01662-5

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