求解非线性优化问题的一个非线性Lagrange函数

A Nonlinear Lagrangian for Nonlinear Optimization

提出了一个求解非凸的具有不等式约束的非线性优化问题的一个非线性Lagrange函数,并讨论了在K-T点的性质。收敛定理表明,在适当的条件下,当参数k大于某一阈值k0时,产生的点列具有局部收敛性,由此给出了与罚参数相关的解的误差估计。

This paper proposes a nonlinear Lagrangian for solving nonconvex, nonlinear optimization problems with inequality constraints. It discusses properties of the function at the K - T point. The convergence theorem shows that the sequence of iterate points generated based on the proposed nonlinear Lagrangian is locally convergent when the penalty k parameter is larger than a threshold k0 under a set of suitable conditions on problem functions, thereby giving the error estimate for the solution, depending on the penalty parameter.