A Merit Function for Inequality Constrained Nonlinear Programming Problems

We consider the use of the sequential quadratic programming (SQP) technique for solving the inequality constrained minimization problem min x f(x) subject to: g i (x) 0; i = 1; : : :; m: SQP methods require the use of an auxiliary function, called a merit function or line-search function, for assessing the steps that are generated. We derive a merit function by adding slack variables to create an equality constrained problem and then using the merit function developed earlier by the authors for the equality constrained case. We stress that we do not solve the slack variable problem, but only use it to construct the merit function. The resulting function is simpliied in a certain way that leads to an eeective procedure for updating the squares of the slack variables. A globally convergent algorithm, based on this merit function, is suggested, and is demonstrated to be eeective in practice.