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本文从古典的Lagrange函数的乘子法入手,通过对惩罚函数法的分析,指出了增广的Lagrange函数在解决带约束非线性规划问题中的重要作用。并在增广的Lagdange目标函数中,介绍了将Lagrange乘子,由常数型乘子增广为函数型乘子,这样就把一系列无约束的最优化问题变成了只有一个约束的优化问题,从而对增广的Lagrange函数在乘子法中的作用进行了扩充。
Starting with the multiplicative method of classical Lagrange function, this paper points out the important role of augmented Lagrange function in solving the nonlinear programming problem with constraint by analyzing the penalty function method. In the augmented Lagdange objective function, the Lagrange multiplier is extended from a constant type multiplier to a functional multiplier, so that a series of unconstrained optimization problems are transformed into a constrained optimization problem , Thus expanding the role of augmented Lagrange function in multiplier method.