A new semi-penalty method for nonlinear programming

Abstract

Semi-penalty function methods, which are proposed by Nie, are new approaches combining sequential quadratic programming (SQP) methods and sequential penalty quadratical programming (SlQP) approaches. But in some cases, the subproblem may be inconsistent in Nie's method. Therefore, we aim to overcome the inconsistence in this paper. We regard some constraints, which is satisfied in some point, as constraints. Other constraints are acted as penalty term. The convergent results are obtained. Further, we extend our new semi-penalty method to augmented Lagrangian penalty approaches.