论文标题
通过双SONC锥和线性编程的全球优化
Global Optimization via the Dual SONC Cone and Linear Programming
论文作者
论文摘要
使用非负电路总和（SONC）的双锥，我们提供了全局优化问题的放松，以最大程度地减少指数总和，作为一种特殊情况，是一种多变量的真实多项式。我们的方法基于两个关键观察。首先，双SONC锥体包含在原始锥中。因此，该锥体中的遏制是非阴性证书。其次，我们表明双锥体中的成员资格可以通过线性程序验证。我们实施了算法，并提出了将我们的方法与现有方法进行比较的初始实验结果。
Using the dual cone of sums of nonnegative circuits (SONC), we provide a relaxation of the global optimization problem to minimize an exponential sum and, as a special case, a multivariate real polynomial. Our approach builds on two key observations. First, that the dual SONC cone is contained in the primal one. Hence, containment in this cone is a certificate of nonnegativity. Second, we show that membership in the dual cone can be verified by a linear program. We implement the algorithm and present initial experimental results comparing our method to existing approaches.
