论文标题
通过Fritz John条件增强的精确多项式优化的符号算法
A symbolic algorithm for exact polynomial optimization strengthened with Fritz John conditions
论文作者
论文摘要
考虑一个多项式优化问题。将Fritz John条件产生的多项式方程式添加到约束集中不会改变最佳值。正如[Arxiv：2205.04254（2022）]中所证明的那样，在某些通用性假设下设置的新约束中，客观多项式具有有限的许多值。基于此，我们提供了一种算法，该算法使我们能够准确地计算此最佳值。我们的方法取决于实际自由基发电机和Gröbner基础的计算。最后，我们应用我们的方法来解决一些数学程序实例，并具有互补性约束。
Consider a polynomial optimization problem. Adding polynomial equations generated by the Fritz John conditions to the constraint set does not change the optimal value. As proved in [arXiv:2205.04254 (2022)], the objective polynomial has finitely many values on the new constraint set under some genericity assumption. Based on this, we provide an algorithm that allows us to compute exactly this optimal value. Our method depends on the computations of real radical generators and Gröbner basis. Finally, we apply our method to solve some instances of mathematical program with complementarity constraints.
