一类非线性优化的Canonical对偶函数

Canonical Duality Function for a Class of Nonlinear Optimization

摘要:

文章研究如何获取球体约束下非线性优化的全局最小点。通过引入常微分方程和构造Canonical对偶函数的局部形式，文章推广完美对偶定理，勾勒出了原问题的KKT点和对偶问题的KKT点两者之间的关系。文章中给出了凸乘子定义、对偶定理和搜寻全局最优点的方法，并通过一些例子加以演示。

Abstract:

How to get a global minimum of a function over a sphere is studied. Differential equation and canonical dual function are introduced to formulate the perfect duality theory, which shows the relationship between the KKT points of the primal problem and the canonical dual problem. Canonical duality theory and other global optimization methods are applied. Examples are given to illustrate the main idea