不等式约束优化问题的Hestenes-Powell增广拉格朗日函数的精确性质

增广拉格朗日函数法是用无约束极小化技术求解约束优化问题的一类重要方法.本文对不等式约束优化问题的Hestenes-Powell增广拉格朗日函数(简记为HP-ALF)的精确性质作了详尽讨论.在适当的假设下,建立了原不等式约束优化问题的极小点和HP-ALF在原问题变量空间或者原问题变量空间与乘子变量空间的积空间上的无约束极小点之间的相互对应关系;获得了关于HP-ALF的精确性的许多新结果.本文给出的性质说明HP-ALF是一个连续可微的精确乘子罚函数,且用经典的乘子法可求得不等式约束优化问题的最优解和对应的拉格朗日乘子值.

Exactness Properties of the Hestenes-Powell Augmented Lagrangian Function for Inequality Constrained Optimization Problems

The Hestenes-Powell augmented Lagrangian function(HP-ALF)has been used for solving inequality constrained optimization problems via unconstrained minimization techniques.Under suitable assumptions,the relationship is established in this paper between the solution of the original inequality constrained optimization problem and the unconstrained minimization of the HP-ALF.Many new results on exactness properties of the HP-ALF are obtained.The properties given in this paper show that the HP-ALF is an exact multiplier penalty function,and a solution of the original inequality constrained optimization problem and the corresponding values of the Lagrange multipliers can be found by the well known method of multipliers.