A discussion on tighter estimate of the duality gap

This paper reviews a key concept in optimization theory, the duality gap, and takes classical unit commitment and economic dispatch problems in power systems as instances to explain its cause. Then, the paper explains the principle of estimating the duality gap in Reference [1] and the inaccuracy that exists. The paper innovatively proposes the idea of using the number of binding constraints to estimate the relative duality gap that expands the current theory. Finally, the paper uses randomly generated computational instances to demonstrate the correctness of the proposed estimation method. A rigorous proof will be provided separately.