求解约束规划的一个非线性Lagrange函数

A nonlinear Lagrangian for constrained programming

提出了一个求解具有不等式约束的非线性规划问题的非线性Lagrange函数.此函数主要用于解决非凸规划问题.讨论了函数在KKT点的性质,收敛定理表明了在适当的条件下,当罚参数大于某一阈值时,产生的点列具有局部收敛性,并给出了与罚参数相关的解的误差估计.此函数的收敛速度较优于Bertsekas提出的指数函数乘子法.

This paper proposes a nonlinear Lagrangian for solving nonlinear programming problems with inequality constraints. The function mainly is studied for nonconvex programming problems. It discusses properties of the function at KKT point. The convergence theorem shows that the sequence of iterate points, which are generated based on the proposed nonlinear Lagrangian, is locally convergent when the penalty parameter is larger than a threshold under a set of suitable conditions on problem functions. Meanwhile the error bound solution, depending on the penalty parameter, is also established. The convergence speed is faster than Bertsekas＇exp-function.