一类不确定凸多项式优化的SOS松弛对偶问题

SOS Relaxation Dual Problem for a Class of Uncertain Convex Polynomial Optimization

考虑一类目标函数和约束函数均具有谱面不确定数据的平方和(SOS)凸多项式优化问题.首先,借助SOS条件建立带有不确定数据的SOS凸多项式系统的择一性定理;其次,引入该SOS多项式优化问题的SOS松弛对偶问题,并刻画它们之间的鲁棒弱对偶性与强对偶性质;最后,借助数值算例说明该SOS松弛对偶问题可以重构为半定规划问题.

We considered a class of sum of squares(SOS)convex polynomial optimization problems with spectrahedral uncertainty data in both objective and constraint functions.Firstly,an alternative theorem for SOS-convex polynomial system with uncertain data was established in terms of SOS conditions.Secondly,we introduced a SOS relaxation dual problem for this SOS polynomial optimization problem and characterized the robust weak and strong duality properties between them.Finally,a numerical example was used to demonstrate that the SOS relaxation dual problem could be reformulated as a semidefinite programming problem.