CAJ | 학술논문

本文对用无约束极小化方法求解等式约束非线性规划问题的Hestenes-Powell增广拉格朗日函数作了进一步研究.在适当的条件下,我们建立了Hestenes-Powell增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系,并且也给出了Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系.因此,从理论的观点来看,原约束问题的解和对应的拉格朗日乘子值不仅可以用众所周知的乘子法求得,而且可以通过对Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上执行一个单一的无约束极小化来获得.
본문대용무약속겁소화방법구해등식약속비선성규화문제적Hestenes-Powell증엄랍격랑일함수작료진일보연구.재괄당적조건하,아문건립료Hestenes-Powell증엄랍격랑일함수재원문제변량공간상적무약속겁소여원약속문제적해지간적관계,병차야급출료Hestenes-Powell증엄랍격랑일함수재원문제변량화승자변량적적공간상적무약속겁소여원약속문제적해지간적일개관계.인차,종이론적관점래간,원약속문제적해화대응적랍격랑일승자치불부가이용음소주지적승자법구득,이차가이통과대Hestenes-Powell증엄랍격랑일함수재원문제변량화승자변량적적공간상집행일개단일적무약속겁소화래획득.
In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques. Under suitable assumptions, the relationship is established between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the space of problem variables and the solution of the original constrained problem, and a relationship is also presented between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers and the solution of the original constrained problem. Therefore, from the theoretical point of view, a solution of the constrained problem and the corresponding values of the Lagrange multipliers can be found not only by the well known method of multipliers but also by performing a single unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers.