带有不等式约束的非线性规划问题的一个精确增广Lagrange函数

对求解带有不等式约束的非线性非凸规划问题的一个精确增广Lagrange函数进行了研究．在适当的假设下，给出了原约束问题的局部极小点与增广Lagrange函数，在原问题变量空间上的无约束局部极小点之间的对应关系．进一步地，在对全局解的一定假设下，还提供了原约束问题的全局最优解与增广Lagrange函数，在原问题变量空间的一个紧子集上的全局最优解之间的一些对应关系．因此，从理论上讲，采用该文给出的增广Lagrange函数作为辅助函数的乘子法，可以求得不等式约束非线性规划问题的最优解和对应的Lagrange乘子．

Exact Augmented Lagrangian Function for Nonlinear Programming Problems With Inequality Constraints

An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed.Under suitable hypotheses,the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem.Furthermore,under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem.Therefore,from the theoretical point of view,a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.