运筹学学报
運籌學學報
운주학학보
OR TRANSACTIONS
2012年
2期
51-64
,共14页
约束非线性规划%精确罚函数%低阶罚函数%光滑精确罚函数%二阶充分条件
約束非線性規劃%精確罰函數%低階罰函數%光滑精確罰函數%二階充分條件
약속비선성규화%정학벌함수%저계벌함수%광활정학벌함수%이계충분조건
constrained nonlinear programming%exact penalty function%lower order penalty function%smooth exact penalty function%second order sufficient condition
对不等式约束优化问题提出了一个低阶精确罚函数的光滑化算法.首先给出了光滑罚问题、非光滑罚问题及原问题的目标函数值之间的误差估计,进而在弱的假设之下证明了光滑罚问题的全局最优解是原问题的近似全局最优解.最后给出了一个基于光滑罚函数的求解原问题的算法,证明了算法的收敛性,并给出数值算例说明算法的可行性.
對不等式約束優化問題提齣瞭一箇低階精確罰函數的光滑化算法.首先給齣瞭光滑罰問題、非光滑罰問題及原問題的目標函數值之間的誤差估計,進而在弱的假設之下證明瞭光滑罰問題的全跼最優解是原問題的近似全跼最優解.最後給齣瞭一箇基于光滑罰函數的求解原問題的算法,證明瞭算法的收斂性,併給齣數值算例說明算法的可行性.
대불등식약속우화문제제출료일개저계정학벌함수적광활화산법.수선급출료광활벌문제、비광활벌문제급원문제적목표함수치지간적오차고계,진이재약적가설지하증명료광활벌문제적전국최우해시원문제적근사전국최우해.최후급출료일개기우광활벌함수적구해원문제적산법,증명료산법적수렴성,병급출수치산례설명산법적가행성.
In this paper,we propose a method to smooth the general lower order exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem,of the nonsmooth penalty problem and of the original optimization problem.It is shown that under mild assumption,an approximate global solution of the original problem can be obtained by searching a global solution of the smoothed penalty problem.We develop an algorithm for solving the original optimization problem based on the smoothed penalty function and prove the convergence of the algorithm.Some numerical examples are given to illustrate the applicability of the present smoothing method.
