SIAM Journal on Optimization, Volume 30, Issue 2, Page 1501-1526, January 2020.
In this paper, we employ advanced techniques of variational analysis and generalized differentiation to examine robust optimality conditions and robust duality for an uncertain nonsmooth multiobjective optimization problem under arbitrary uncertainty nonempty sets. We establish necessary and sufficient optimality conditions for (local) robust (weakly) efficient solutions of the considered problem. Our problem involves nonsmooth real-valued functions and data uncertainty in both the objective and constraint functions, and its necessary and sufficient optimality conditions are exhibited in terms of multipliers and the Mordukhovich or Clarke subdifferentials of the related functions. Moreover, we formulate a dual multiobjective problem to the underlying program and examine robust weak, strong, and converse duality relations between the primal problem and its dual under assumptions of (strictly) generalized convexity.

中文翻译：

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数据不确定性下多目标优化问题的鲁棒最优性和对偶性

SIAM优化杂志，第30卷，第2期，第1501-1526页，2020年1月。
在本文中，我们采用变分分析和广义微分的先进技术，研究了任意不确定非空集下不确定非光滑多目标优化问题的鲁棒最优条件和鲁棒对偶性。我们为所考虑问题的（局部）健壮（弱）有效解决方案建立了必要和充分的最优条件。我们的问题涉及目标函数和约束函数中的非光滑实值函数和数据不确定性，并且根据相关函数的乘数和Mordukhovich或Clarke次微分，显示了其充要条件。此外，我们为基础程序制定了一个双重多目标问题，并研究了鲁棒的弱，强，