半代数函数的正性与optimization
Positivity and optimization for semi-algebraic functions
摘要：
我们描述了代数证书的积极性属于一个生成代数的博雷尔可测函数的功能，特别强调代数生成的半代数函数。在这种情况下，具有由相同代数的元素给出的约束的标准全局最优化问题经由变量的自然变量变换被简化为多项式优化的更好理解的情况。一系列简单的例子和数值实验补充了文章的理论部分。
英文摘要：
We describe algebraic certificates of positivity for functions belonging to a finitely generated algebra of Borel measurable functions, with particular emphasis to algebras generated by semi-algebraic functions. In which case the standard global optimization problem with constraints given by elements of the same algebra is reduced via a natural change of variables to the better understood case of polynomial optimization. A collection of simple examples and numerical experiments complement the theoretical parts of the article.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
