论文标题
二重多项式优化的Lagrange乘数表达方法
A Lagrange Multiplier Expression Method for Bilevel Polynomial Optimization
论文作者
论文摘要
本文研究了双线性多项式优化问题。为了解决它们，我们提供了一种基于多项式优化弛豫的方法。每种放松都是从较低级优化的Kurash-Kuhn-Tucker（KKT）条件获得的，用于半侵入式编程的交换技术。对于KKT条件，Lagrange乘数表示为多项式或有理功能。力矩SOS松弛用于解决多项式优化弛豫。在某些一般假设下，我们证明了用于解决双层多项式优化问题的算法的收敛性。提出了数值实验以显示该方法的效率。
This paper studies bilevel polynomial optimization problems. To solve them, we give a method based on polynomial optimization relaxations. Each relaxation is obtained from the Kurash-Kuhn-Tucker (KKT) conditions for the lower level optimization and the exchange technique for semi-infinite programming. For KKT conditions, Lagrange multipliers are represented as polynomial or rational functions. The Moment-SOS relaxations are used to solve the polynomial optimizattion relaxations. Under some general assumptions, we prove the convergence of the algorithm for solving bilevel polynomial optimization problems. Numerical experiments are presented to show the efficiency of the method.
