Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: "yes" and "very well", respectively.

中文翻译：

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线性优化对线性优化问题有用吗？

线性优化考虑线性规划问题，但不是尝试用线性优化方法解决它们，而是采用扰动弹性可行性寻求算法，并将它们引向减少的（不一定是最小的）目标函数值。我们开始通过实验探索的两个问题是 (i) 线性优越性是否提供了一个可行点，其线性目标函数值低于在相同条件下运行相同的可行性寻求算法而没有优越性？(ii) 与解决线性规划问题的单纯形方法相比，线性优化的表现如何？根据我们在此介绍的计算实验，这两个问题的答案分别是：“是”和“非常好”。