非可微r-不变凸函数的η-鞍点条件

η -saddle Point Condition for Non-differentiable r -invexity Functions

利用η-逼近法,定义了η-鞍点和η-Lagrange函数。研究了一类包含r-不变凸函数的非线性数学规划问题的鞍点条件,得到了η-近似优化问题下的η-鞍点最优性准则和原规划的最优解与η-近似优化问题下的η-Lagrange鞍点的等价性,用新的方法推广了相关鞍点结论。

This paper uses theη-approximation method to define theη-saddle point andη-Lagrange functions.The saddle point conditions of a class of nonlinear mathematical programming problems including r-invex functions are studied,and theη-saddle point optimality criterion under theη-approximation optimization problem and the optimal solution of the original program and the equivalence of theη-Lagrange saddle point under theη-approximation optimization problem are obtained,and the relevant saddle point conclusion is generalized by the new method.