A Globally Convergent Penalty-Free Method for Optimization with Equality Constraints and Simple Bounds

In this paper, we propose an algorithm for the solution of nonlinear constrained programming. This algorithm does not use any penalty function or a filter. Instead, it uses the idea of maximal constraint violation to guarantee global convergence. The infeasibility of each iterate is controlled by a progressively decreasing limit. At each iteration, a normal step which is obtained by solving a tightened normal subproblem and a tangential step which is a solution of a tangential subproblem are computed successively. The algorithm reduces the value of objective function or improves feasibility according to the relation of the tangential predicted reduction and the predicted reduction of constraint violation achieved by the trial step. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness of iterate sequence. Moreover, the algorithm does not need any restoration phase. We also include some preliminary yet promising numerical results on some standard test problems in constrained optimization.