求解不等式约束问题的一类新的精确罚函数方法  

A NEW EXACT PENALTY FUNCTION METHOD FOR SOLVING INEQUALITY CONSTRAINED PROBLEMS

作　　者：许雨晴 周芳宇 刘茜 Xu Yuqing;Zhou Fangyu;Liu Qian(School of Mathematics and Statistics,Shandong Normal University,250358,Jinan,China)

机构地区：[1]山东师范大学数学与统计学院,济南250358

出　　处：《山东师范大学学报（自然科学版）》2018年第4期406-413,共8页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11271226;11271233)

摘　　要：对于光滑的非线性不等式约束优化问题,我们提出了一类新的精确罚函数,并给出了罚函数的精确性质的充分条件.在实际应用过程中,优化问题的可行域可能是空集.因此,本文在考虑了问题可能不可行的前提下,讨论了精确罚函数方法,并分析了其全局收敛性.最后通过数值实验,证明了该算法对于不同类型的罚函数是有效的.For smooth nonlinear inequality constrained optimization problems,we propose a new class of exact penalty functions,and develop the sufficient conditions for exact penalty property.In the process of actual application,the feasible domain of optimization problem may be empty.Therefore,in this paper,the exact penalty function method is discussed and its global convergence is analyzed assuming that the problem may not be feasible.Finally,through numerical experiments,it is proved that the algorithm is reliable for different exact penalty functions.

关 键 词：全局最优 不等式约束优化 精确罚函数 不可行性 算法 

分 类 号：O221.2[理学—运筹学与控制论]