Recently, Bouafia et al. (J Optim Theory Appl 170:528–545, 2016) investigated a new efficient kernel function that differs from self-regular kernel functions. The kernel function has a trigonometric barrier term. This paper introduces a new efficient twice parametric kernel function that combines the parametric classic function with the parametric kernel function trigonometric barrier term given by Bouafia et al. (J Optim Theory Appl 170:528–545, 2016) to develop primal–dual interior-point algorithms for solving linear programming problems. In addition, we obtain the best complexity bound for large and small-update primal–dual interior point methods. This complexity estimate improves results obtained in Li and Zhang (Oper Res Lett 43(5):471–475, 2015), Peyghami and Hafshejani (Numer Algorithms 67:33–48, 2014) and matches the best bound obtained in Bai et al. (J Glob Optim 54:353–366) and Peng et al. (J Comput Technol 6:61–80, 2001). Finally, our numerical experiments on some test problems confirm that the new kernel function has promising applications compared to the kernel function given by Fathi-Hafshejani (Optimization 67(10):1605–1630, 2018).

中文翻译：

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高效的二次参数化三角函数，用于线性优化

最近，Bouafia等。（J Optim Theory Appl 170：528–545，2016）研究了一种新的有效内核函数，该函数不同于自规则内核函数。核函数具有三角势垒项。本文介绍了一种新的高效两次参数核函数，该函数将参数经典函数与Bouafia等人给出的参数核函数三角障碍项相结合。（J Optim Theory Appl 170：528–545，2016）开发用于解决线性规划问题的原始对偶内点算法。此外，对于大型和小型更新的原始对偶内点方法，我们获得了最佳的复杂度范围。这种复杂性估算可改善在Li和Zhang（Oper Res Lett 43（5）：471–475，2015），Peyghami和Hafshejani（Numer算法67：33-48，2014年），并与Bai等人获得的最佳界限匹配。（J Glob Optim 54：353–366）和Peng等。（J Comput Technol 6：61–80，2001）。最后，我们对一些测试问题的数值实验证实，与Fathi-Hafshejani提供的内核函数相比，新的内核函数具有广阔的应用前景（Optimization 67（10）：1605–1630，2018）。