调和函数理论在二维优化问题中的应用  

APPLICATION OF HARMONIC FUNCTION'S THEORY IN TWO-DIMENSION OPTIMIZATION PROBLEM

作　　者：张静[1] 史文谱[2,1] ZHANG Jing;SHI WenPu(Department of Mechanical and Electrical Engineering,Yantai Automobile Engineering Professional College,Yantai 265500,China;School of Mechatronics and Automobile Engineering,Yantai University,264005,China;Key Laboratory of Advanced Manufacturing and Control Technology in Universities of Shandong,Yantai University,264005,China)

机构地区：[1]烟台汽车工程职业学院机电工程系,烟台265500 [2]烟台大学机电汽车工程学院,烟台264005

出　　处：《机械强度》2018年第4期890-894,共5页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(11672301);山东省科技攻关项目(2012G0030011)资助

摘　　要：许多工程问题的数学模型常常归结为二维优化问题,寻求高效率和高精度的优化方法一直是人们研究的热点问题之一。利用调和函数的性质和格林定理研究了调和函数的内点取值与其边界值的关系,说明了其极值的非局域性特点。当二维优化问题的目标函数是调和函数时,其二维寻优将简化为在其有限可行域边界上的一维搜索问题。最后通过四个算例说明了方法的可行性。研究思路和结论可有效推广到三维优化问题的求解。The mathematical models of many engineering problems can often come down to two-dimensional optimization problems,it has been one of the hot issues of seeking the high effective and precision optimizing method.The characteristics of harmonic function and Green theory were used to study the relations between the values of harmonic function and its boundary values,and demonstrate the non-locality of its extreme value.When the objective function of the optimization is harmonic function,the two-dimensional optimization can be simplified as a one-dimensional optimization on the boundary of its feasible region.At last,three examples were given to show the feasibility of the method here.The research ideas and the conclusions can be generalized to the solution of the three-dimensional optimization problems.

关 键 词：二维优化问题 调和函数 可行域边界 最大值 一维搜索 

分 类 号：O224[理学—运筹学与控制论]