Minimax规划及更复杂的min-max-min规划是一类典型的非凸非光滑优化问题，在科学与工程领域中广泛应用．考虑到实际应用中的这类模型常含大量的分量函数，本课题拟给出含大量分量函数的minimax规划与min-max-min规划的高效率数值解法，具体包含以下三方面的工作：(1) 对大量分量函数组成的max函数，构造一类含积极集策略的光滑化max函数并分析其性质．(2) 设计光滑化参数的自适应更新策略及迭代解的精度改进策略来改善光滑化算法潜在的病态问题．(3) 对含大量分量函数的minimax规划与min-max-min规划，给出高效率的光滑化算法，证明算法的收敛性，设计软件并用于解决实际问题．本项目的研究不仅丰富了光滑化max函数、光滑化算法及非凸非光滑优化问题的研究，而且积极集策略直接引入到光滑化函数的方式使相应的光滑化算法可以在更弱的条件下建立收敛性，因而适用于更广泛的问题．

The minimax programming and more complicated min-max-min programming, are a typical class of nonconvex and nonsmooth optimization, and widely applied in the fields of science and engineering. Since these problems always have many component functions,this project will present efficient algorithms for solving the minimax programming and min-max-min programming involving many component functions. There are three parts included:(1) For the maximum function with many component functions, we will give a class of smoothing functions with the active set strategy, and study their properties. (2) To improve the ill-conditioned problem of smoothing methods, we will give the adaptive updating strategies of the smoothing parameter and the strategies to get high accuracy iterative solution.(3) For the minimax programming and min-max-min programming involving many component functions, we will present efficient algorithms with convergence analysis and software, and apply them to solve practical problems. This research of this project will not only make contributions to smoothing maximum functions, smoothing methods, nonconvex and nonsmooth optimization,but also give efficient algorithms with weak convergence conditions due to the ways of introducing the active set strategy to the smoothing function.