论文标题
错误界限，面部残留功能以及指数锥的应用
Error bounds, facial residual functions and applications to the exponential cone
论文作者
论文摘要
我们构建了一个通用框架，用于为圆锥可行性问题得出错误范围。特别是，我们的方法允许一个人使用无法正常的锥体，甚至没有可计算的预测，这是两个以前具有挑战性的障碍。出于此目的，我们首先显示如何使用称为一步面部残留功能的对象构建误差界限。然后，我们开发了几种工具来计算这些面部残留功能，即使没有对锥体上的投影的封闭形式表达式。我们通过计算指数可行性问题的紧密误差界来证明结果的使用和功能。有趣的是，我们发现了一个自然的例子，该示例与Boltzmann-Shannon熵有关的最紧密误差绑定。我们还能够产生一个hölderian错误绑定的集合的示例，但是一组可允许的指数的最高限制本身并不是可允许的指数。
We construct a general framework for deriving error bounds for conic feasibility problems. In particular, our approach allows one to work with cones that fail to be amenable or even to have computable projections, two previously challenging barriers. For the purpose, we first show how error bounds may be constructed using objects called one-step facial residual functions. Then, we develop several tools to compute these facial residual functions even in the absence of closed form expressions for the projections onto the cones. We demonstrate the use and power of our results by computing tight error bounds for the exponential cone feasibility problem. Interestingly, we discover a natural example for which the tightest error bound is related to the Boltzmann-Shannon entropy. We were also able to produce an example of sets for which a Hölderian error bound holds but the supremum of the set of admissible exponents is not itself an admissible exponent.
