论文标题
Lasserre的层次结构的融合：一般情况
Convergence of Lasserre's hierarchy: the general case
论文作者
论文摘要
Lasserre的力矩层次结构包括近似的广义力矩问题（GMP）的实例，其中矩松弛和平方之和的总和（SOS）Strenghtenings沸腾到凸出半际编程（SDP）问题。由于初始GMP的一般性，该技术的应用是无数的，其中一个人可以引用多项式优化问题（POP），最佳控制问题（OCP），音量计算问题，稳定性设置近似问题以及求解非线性部分偏差方程（PDE）。然后用其矩序列的有限截断将原始GMP的解决方案近似。对于每个应用程序，证明这些截短的收敛到最佳力矩序列可以使问题有价值的见解，包括将放松值收敛到原始GMP的最佳值。本说明提出了这种融合的一般证明，无论人们在简单的标准假设下都面临的问题。作为此证明的副产品，一个人在无限的尺寸GMP及其有限的尺寸弛豫中还获得了强大的二元性能。
Lasserre's moment-SOS hierarchy consists of approximating instances of the generalized moment problem (GMP) with moment relaxations and sums-of-squares (SOS) strenghtenings that boil down to convex semidefinite programming (SDP) problems. Due to the generality of the initial GMP, applications of this technology are countless, and one can cite among them the polynomial optimization problem (POP), the optimal control problem (OCP), the volume computation problem, stability sets approximation problems, and solving nonlinear partial differential equations (PDE). The solution to the original GMP is then approximated with finite truncatures of its moment sequence. For each application, proving convergence of these truncatures towards the optimal moment sequence gives valuable insight on the problem, including convergence of the relaxed values to the original GMP's optimal value. This note proposes a general proof of such convergence, regardless the problem one is faced with, under simple standard assumptions. As a byproduct of this proof, one also obtains strong duality properties both in the infinite dimensional GMP and its finite dimensional relaxations.
