A characterization for tightness of the sparse Moment-SOS hierarchy
研究了求解稀疏多项式优化问题的稀疏矩-SOS松弛层次结构，给出了该层次结构紧性的充要条件，并基于此提出了若干充分条件。
Abstract This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative polynomials, each of which belongs to the sum of the ideal and quadratic module generated by the corresponding sparse constraints. Based on this characterization, we give several sufficient conditions for the sparse Moment-SOS hierarchy to be tight. In particular, we show that this sparse hierarchy is tight under some assumptions such as convexity, optimality conditions or finiteness of constraining sets.