A Filter SQP Algorithm For Nonlinear Constrained Optimization Based On Augmented Lagrangian Functions

In this thesis, nonlinear constrained optimization problems are inves-tigated. These problems abound in many fields, for instance, engineering, national defence, economy society and social sciences, etc. Therefore, the research on new theory and efficient numerical algorithms for nonlinear con-strained optimization problems has important theoretical significance and practical value.Based on the idea of augmented Lagrangian methods and filter tech-nologies, and on steering technologies designed for exact penalty function-s, by using an adaptive strategy for the penalty parameters and multipliers, combined with a backtracking line search technique, we propose a filter SQP algorithm based on augmented Lagrangian functions in this thesis. In each iteration of the proposed algorithm, the search direction is defined as a con-vex combination of a steering step and a predictor step under some certain conditions, where the steering step represents the best local improvemen-t in constraint violation, and prediction step represents the biggest predict-ed reduction of augmented Lagrangian function of quadratic approximation model. Thus, the search direction always contains information from both the constraint violation and augmented Lagrangian function. In the stage of backtracking line search, by using a penalty model, our proposed method replaces the traditional restoration phase with a penalty mode. Under appro-priate assumptions, we prove that the proposed algorithm is well-posed. And under some mild assumptions, we prove the global convergence of our algo-rithm. At the same time, the numerical tests validate our method by using MATLAB for a set of test problems.