In this paper, a new class of kernel functions is introduced. We show that most existing kernel functions belong to this class. All functions in the new class are eligible in the sense of Bai et al. (SIAM J Optim 15(1):101–128, 2004), and hence the analysis of the resulting interior-point methods can follow the scheme proposed in Bai et al. (2004). We introduce five new kernel functions and by using this scheme we show that primal-dual IPMs based on these functions enjoy the best known iteration bound for large-update methods, i.e., \(O(\sqrt{n}\log n\log \frac{n}{\epsilon }).\) Finally, to demonstrate the efficiency of IPMs based on the new kernel functions, some numerical results are provided.

本文介绍了一类新的内核函数。我们表明大多数现有的内核函数都属于此类。在Bai等人的意义上，新类中的所有函数都可以使用。（SIAM J Optim 15（1）：101–128，2004），因此对所得内点方法的分析可以遵循Bai等人提出的方案。（2004）。我们介绍了五个新的内核函数，并且使用这种方案，我们证明了基于这些函数的原始对偶IPM享有大型更新方法的最著名迭代约束，即\（O（\ sqrt {n} \ log n \ log \ frac {n} {\ epsilon}）。\）最后，为了演示基于新内核函数的IPM的效率，提供了一些数值结果。