首页 | 本学科首页   官方微博 | 高级检索  
     检索      


A note on optimization using the augmented penalty function
Authors:V Raghavendra  K S P Rao
Institution:1. Department of Mathematics, Indian Institute of Technology, Kanpur, India
2. Department of Electrical Engineering, Indian Institute of Technology, Kanpur, India
Abstract:The augmented penalty function is used to solve optimization problems with constraints and for faster convergence while adopting gradient techniques. In this note, an attempt is made to show that, ifx* ∈S maximizes the function $$W(x,\lambda ,{\rm K}) = f(x) - \sum\limits_{j = 1}^n {\lambda _j C_j (x)} - K\sum\limits_{j = 1}^n {C_j ^2 (x)} ,$$ thenx* maximizesf(x) over all thosexS such that $$C_j (x) \leqslant C_j ,j = 1,2, \ldots ,n,$$ under the assumptions that the λ j 's andk are nonnegative, real numbers. Here,W(x, λ,K),f(x), andC j (x),j=1, 2,...,n, are real-valued functions andC j (x) ≥ 0 forj=1, 2,...,n and for allx. The above result is generalized considering a more general form of the augmented penalty function.
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号