摘要
对于等式约束的非线性规划问题,一般的解决方法是在每次迭代中更新拉格朗日乘子且逐渐增大拉格朗日函数的惩罚因子,当罚因子充分大或充分接近局部最优解时,二阶充分条件是满足的;对不等式约束问题也采用了相应的方法.在凸的情况下,对于任意的罚因子或者在每次迭代中不要求精确极小化,就能全局收敛到最优解;证明了拉格朗日乘子是收敛的.
As for nonlinear programming gradually increase penalty factor of Lagrange problem with equality constraints, a general method of solution is to function and to renew Lagrange multipliers in the iteration of each cycle, if penalty factor is sufficiently large or is close to local optimal solution, the second-order sufficient conditions are satisfied. This paper uses the corresponding method for inequality-constrained problems. Global convergence to an optimal solution is established in the convex case for an arbitrary penalty factor or without the requirement of an exact minimization in the iteration of each cycle. Furthermore, the Lagrange multipliers are proved to converge.
出处
《重庆工商大学学报（自然科学版）》
2013年第4期13-16,共4页
Journal of Chongqing Technology and Business University:Natural Science Edition
关键词
非线性规划
增广拉格朗日函数
拉格朗日乘子收敛
nonlinear programming
the Augmented Lagrange Function
convergence of Lagrange multipliers
