简单光滑精确指数乘子罚函数

Simple Smooth Exact Exponential Multiplier Penalty Function

解决有约束非线性规划问题的一个基本方法是将之简化为无约束问题,比如罚函数法.其中精确罚函数法是通过解决某个无约束问题来获得原有约束问题的一个解.就经典的罚函数定义而言,简单精确罚函数是非光滑的,从而难以处理.作者提出一个简单光滑精确指数乘子罚函数,验证在二阶充分条件下它存在相应的超线性收敛率,并得到关于它的强弱对偶结果.

One of the fundamental methods for solving constrained nonlinear programming problems is to reduce it into unconstrained problems,such as penalty function methods. The exact penalty function method is to obtain a solution of the original problem by solving a single unconstrained programming problem.When the traditional definition of penalty functions is used,the simple exact penalty function is nonsmooth,thus it is difficult to deal with.In this paper,a simple smooth exact exponential multiplier penalty function is proposed.A superlinear convergence rate is obtained under the second order sufficient condition.Weak and strong duality results are also established.