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arXiv · 1906.06656

Characterization of the norm-based robust solutions in vector optimization

Morteza Rahimi·Majid Soleimani-damaneh
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Abstract

In this paper, we study the norm-based robust (efficient) solutions of a Vector Optimization Problem (VOP). 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 (CQ). We extend the provided characterization to VOPs with conic constraints. Moreover, we derive a necessary condition for norm-based robustness utilizing a nonsmooth gap function.

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Morteza Rahimi, Majid Soleimani-damaneh. 2019-06-16. Characterization of the norm-based robust solutions in vector optimization. https://arxiv.org/abs/1906.06656

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