具有多值映射的两级优化问题的广义算法研究  

Study on generalized algorithm for two-level optimization problems with multi-value map

作　　者：向丽[1] 顾培亮[1] 

机构地区：[1]天津大学系统工程研究所,天津300072

出　　处：《系统工程学报》2003年第3期193-197,共5页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(79770060).

摘　　要：两级优化问题是一种非凸非光滑问题,绝大多数问题的求解都是建立在下层有唯一解的基础之上的。而本文针对多值映射,即下层非唯一解的情形,利用隐函数理论,将两级优化问题转化为带有隐函数的非光滑问题,提出求解这类问题的广义算法框架,并证明其收敛性,最后通过实例验证该方法的实用性.Bi_level optimization problems are a kind of non_convex and nonsmooth problem. Solving most of these problems is based on the unique lower level solutions. In the paper, a generalized algorithm structure is presented for bi_level optimization problems with nonunique lower level solutions based on the implicit function theory. First, the problem is converted to a nonsmooth problem with an implicit function. Afterwards the convergence proof of generalized algorithm is given. At last, the numerical computation results indicate that this method is efficient and solvable.

关 键 词：递阶优化问题 两级优化问题 广义算法 隐函数理论 多值映射 非凸非光滑问题 

分 类 号：O224[理学—运筹学与控制论]