论文标题
多项式优化的多度
Multi-Degrees in Polynomial Optimization
论文作者
论文摘要
我们研究了多项式目标函数和多项式平等约束的结构化优化问题。该结构来自多个变量的多项式环上的多个分级。对于固定的多重度，我们确定复杂临界点的通用数量。这是对优化问题代数复杂性的衡量标准。我们还讨论来自数值非线性代数的计算和认证方法。
We study structured optimization problems with polynomial objective function and polynomial equality constraints. The structure comes from a multi-grading on the polynomial ring in several variables. For fixed multi-degrees we determine the generic number of complex critical points. This serves as a measure for the algebraic complexity of the optimization problem. We also discuss computation and certification methods coming from numerical nonlinear algebra.
