一类实多元多项式的全局优化的解的边界估计

A Method for Estimating the Bounds of a Real Valued Polynomial's Global Minimizers

对全局最小化问题p：min x∈R^n {P（x）}，P（x）：R^n→R，估计了其最优点的开球的半径a，使得在｜｜x｜｜≤a内，该问题存在全局最小点。同时，也证明了该问题在一定条件下可转化为约束优化问题，并可以通过一系列半正定规划来逼近。

This paper considers the problem of finding the unconstrained global minimum of a real valued polynomial p(x):Rn→R. The problem of estimating the bounds of global minimizers can be solved by some positive semi-definite programs. It is shown that the unconstrained global optimization reduces some constrained optimizations which can be approximated by solving some positive semi-definite programs.