Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems
研究了上下层目标与约束均为多项式的双层优化问题，提出用半定规划松弛序列求解全局最优解并证明收敛性，对凸与非凸下层问题分别给出不同处理方案。
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper-and the lower-level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a convex lower-level problem involves solving a transformed equivalent single-level problem by a sequence of SDP relaxations, whereas our approach for general problems involving a nonconvex polynomial lower-level problem solves a sequence of approximation problems via another sequence of SDP relaxations.