The problem of handling inequality constraints is a difficult task in power system optimization analysis. The equality constraints of an optimization problem are slackened according to the theories of Lagrange function saddle point

so that the primal problem and the corresponding dual problem considering equality constraints are introduced. By defining the saddle space between the primal and dual problem and distributing the saddle space among inequality constraints

the modified equations in allusion to the Lagrange multipliers of inequality constraints are put forward. Furthermore

different optimization algorithms will come into being. The derivation shows that the interior point function method is just a particular case of Lagrange saddle point theory's application. The proposed method can be applied in power system optimization analysis

especially for the task of maximum transmission ability of power system. The calculation result in IEEE 30-bus system and comparison of the result among different algorithms in IEEE 14-bus system demonstrate that the method is effective for handling the problems of load flow inequality constraints.