We revisit the classic supporting hyperplane illustration of the duality gap for non-convex optimization problems. It is refined by dissecting the duality gap into two terms: the first measures the degree of near-optimality in a Lagrangian relaxation, while the second measures the degree of near-complementarity in the Lagrangian relaxed constraints. We also give an example of how this dissection may be exploited in the design of a solution approach within discrete optimization.

中文翻译：

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剖析二元性差距：重新审视支持超平面解释

我们重新审视非凸优化问题对偶间隙的经典支持超平面图解。它通过将二元性差距分解为两个术语来改进：第一个测量拉格朗日松弛中的接近最优的程度，而第二个测量拉格朗日松弛约束中的接近互补的程度。我们还举例说明了如何在离散优化中的解决方案方法的设计中利用这种剖析。