对数平均值的极小积问题

Minimizing Products of Logarithmic Means

考虑一类含参数对数平均值的极小积问题．利用对数平均值不等式，问题转述为不含对数的参数规划问题．作为它们的应用，如果涉及的函数均为线性齐次、约束集为凸多面体（无论有界或无界），则必存在最优解并且可以在其极点处实现．

The minimization of products of logarithmic means containning parameters is considered.By means of logarithmic mean inequality,the problem is transformed into a minimization problem of parametric programmings.As an application,a vertex optimal solution is obtained,if the functions are linear homogeneous and with a polytope constraint set (bounded or unbounded).