ERROR BOUNDS FOR POLYNOMIAL MINIMIZATION OVER THE HYPERCUBE-SIMPLOIDS

作者：Zhang, Yue; Jia, Zhi-Qiang; Zhu, Chun-Gang^*

来源：Pacific Journal of Optimization, 2018, 14(2): 193-210.

• polynomial optimization
• multivariate Bernstein approximation
• hypercube
• simploids
• semidefinite programming

In this paper, based on Schmudgen's Positivstellensatz, we derive explicit error bounds for the hierarchy of semidefinite programming approximations to the problem of minimizing a polynomial over the hypercube-simploids [0,1](n) x Delta(s). Following the methodology of De Klerk and Laurent, we provide bounds for the relaxations and degree bounds for positivity certificates on the hypercube-simploids by using the properties of multivariate Bernstein approximation on the hypercube and simplex. Our results include some results of error bounds of minimizing a polynomial over hypercube and simplex.

• 出版日期2018
• 单位大连理工大学