具有多值映射的两级优化问题的广义算法研究

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．

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

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.