关于一类非光滑极大极小问题的非单调线性搜索算法(英文)

A Nonmonotone Line Search Algorithm for Nonsmooth Discrete Minimax Problem

考虑一类非光滑的离散的极大极小问题 :minmax{fi(x) |i=1…m} ,其中fi 是凸的 ,但不一定可微 .在这里我们给出了非单调线性搜索算法 ,并证明了在一定条件下算法具有全局收敛性 .

A class of nonsmooth discrete minimax problems min max{f_i(x)|i=1,...,m} are considered in this paper, where each f_i is convex, but not necessarily differentiable. The nonmonotone line search algorithm for nonsmooth optimization given by Pang is extended to this case, and we prove that the algorithm is globally convergent.