Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests
Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests Supporting Global Numerical Optimization of Rational Functions by Generic Symbolic Convexity Tests
复制标题
Konrad-zuse-zentrum F ¡ Ur Informationstechnik Berlin 通过通用符号凸性测试支持有理函数的全局数值优化 通过通用符号凸性测试支持有理函数的全局数值优化
DOI：
--
复制
发表时间：
--
期刊：
影响因子：
--
通讯作者：
Stefan Vigerske
中科院分区：
文献类型：
--
作者：
W. Neun;T. Sturm;Stefan Vigerske
凸性是非线性优化中的一个重要性质，因为它允许应用有效的局部方法来寻找全局解。我们提出用符号方法来证明或反驳多面体区域上有理函数的凸性。我们的算法将凸性问题归结为实量词消除问题。我们的方法已在开源计算机代数系统REDUSE中实现并公开可用。我们的长期目标是将Reducts作为符号计算的“主力”集成到数值求解器中。
Convexity is an important property in nonlinear optimization since it allows to apply efficient local methods for finding global solutions. We propose to apply symbolic methods to prove or disprove convexity of rational functions over a polyhedral domain. Our algorithms reduce convexity questions to real quantifier elimination problems. Our methods are implemented and publicly available in the open source computer algebra system Reduce. Our long term goal is to integrate Reduce as a " workhorse " for symbolic computations into a numerical solver.