一类非线性优化的Canonical对偶函数

Canonical Duality Function for a Class of Nonlinear Optimization

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,引入了相应的对偶定理,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.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.

It is studied how to get a global minimum of a function over a sphere. A differential equation is introduced to construct canonical dual function. The corresponding perfect duality theory is established to show the relationship between the KKT points of the primal problem and the canonical dual problem. A new definition on canonical convex multiplier is given with a canonical dual method for the primal problem. Some examples are illustrated.