Abstract
Dual, penalty and multiplier methods are typical methods for solving both equality-and inequality-constrained minimizing problems. The characteristics of these solution methods have not been very clear. A unified geometrical interpretation for these solution methods is given in this paper. The geometrical interpretation has sharpened the characteristics of each solution method. The following conclusion is obtained. The application of the dual method is in general limited to convex programming problems: the penalty method can be applied to nonconvex programming problems, but may suffer from computational instability; and the multiplier method is superir to the other two methods in that it can be applied to nonconvex programming problems without suffering from computational instability.
