Bilevel optimization problems embed the optimality conditions of a sub-problem into the constraints of another optimization problem. We introduce the concept of near-optimality robustness for bilevel problems, protecting the upper-level solution feasibility from limited deviations at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of generic bilevel problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of the proposed algorithm and the impact of valid inequalities on the solution time.

中文翻译：

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接近最优的鲁棒双层优化

双层优化问题将一个子问题的最优条件嵌入到另一个优化问题的约束中。我们为双层问题引入了接近最优稳健性的概念，保护上层解决方案的可行性不受下层有限偏差的影响。对于一般双层问题的近乎最优鲁棒版本，推导了解存在的一般性质和必要条件。当较低级别是凸的时，定义了基于对偶的解决方案方法，利用来自稳健和双层文献的方法。数值结果评估了所提出算法的效率以及有效不等式对求解时间的影响。