近似逼近l_1精确罚函数的罚函数  

Approximately Asymptotic Methods to l_1 Exact Penalty Function

作　　者：连淑君[1] 

机构地区：[1]曲阜师范大学运筹与管理学院,山东日照276826

出　　处：《应用数学》2010年第2期363-369,共7页Mathematica Applicata

基　　金：山东省中青年科学家基金资助项目(2008BS10003);国家自然科学基金资助项目(10971118)

摘　　要：本文对可微非线性规划问题提出了一类新的近似渐近算法与一类渐近算法,它们都是基于一类逼近l1精确罚函数的罚函数而提出的.并证明了近似算法所得序列若有聚点则其为原问题的最优解;若所得序列为无界的,则给出了序列值收敛到最优值的一个充分条件.对渐近算法,在弱的假设条件下,证明了算法所得的极小点列有界,且其聚点均为原问题的最优解.并在Mangasarian-Fromovitz约束条件下,证明了有限次迭代之后,所有迭代均为可行的,即迭代所得的极小点为可行点.In this paper,the author proposes a new approximately asymptotic method and an asymptotic method which are based on a family of penalty function that approximate asymptotically the usual exact penalty function for the differentiable nonlinear programming problem.For the approximately asymptotic method,if the minimizer sequence generated by the algorithm is bounded,the author proves that its accumulation points are optimal solutions of primal problem.If the minimizer sequence generated by the algorithm is unbounded,a sufficent condition is given which can garantee the sequence converges to an optimal solution.For the asymptotic method,under the weak conditions,the author proves that the minimizer sequence generated by the algorithm is bounded,and its accumulation points are optimal solutions of primal problem.Under the Mangasarian-Fromovitz constraint qualification,the author shows that all iterates will remain feasible after a finite number of iterations.

关 键 词：可行点 罚函数 精确罚函数 

分 类 号：O221.2[理学—运筹学与控制论]