运筹学学报
運籌學學報
운주학학보
OR TRANSACTIONS
2012年
2期
9-22
,共14页
修正罚函数%光滑化逼近%低阶罚函数%不等式约束优化问题
脩正罰函數%光滑化逼近%低階罰函數%不等式約束優化問題
수정벌함수%광활화핍근%저계벌함수%불등식약속우화문제
modified penalty function%smoothing approximation%lower order penalty function%inequality-constrained optimization problem
针对不等式约束优化问题,给出了通过二次函数对低阶精确罚函数进行光滑化逼近的两种函数形式,得到修正的光滑罚函数.证明了在一定条件下,当罚参数充分大时,修正的光滑罚问题的全局最优解是原优化问题的全局最优解.给出的两个数值例子说明了所提出的光滑化方法的有效性.
針對不等式約束優化問題,給齣瞭通過二次函數對低階精確罰函數進行光滑化逼近的兩種函數形式,得到脩正的光滑罰函數.證明瞭在一定條件下,噹罰參數充分大時,脩正的光滑罰問題的全跼最優解是原優化問題的全跼最優解.給齣的兩箇數值例子說明瞭所提齣的光滑化方法的有效性.
침대불등식약속우화문제,급출료통과이차함수대저계정학벌함수진행광활화핍근적량충함수형식,득도수정적광활벌함수.증명료재일정조건하,당벌삼수충분대시,수정적광활벌문제적전국최우해시원우화문제적전국최우해.급출적량개수치례자설명료소제출적광활화방법적유효성.
In this paper,two function forms of quadratic smoothing approximation to the lower order exact penalty function are proposed to generate modified smooth penalty functions for inequality-constrained optimization problems.It is shown that under certain conditions,any global minimizer of the modified smooth penalty problem is a global minimizer to the original constrained optimization problem when the penalty parameter is sufficiently large.Two numerical examples are given to show the effectiveness of the present smoothing scheme.
