Two SQP Algorithms Without A Penalty Function Or A Filter For Inequality Constrained Optimization

In this thesis, optimization problems with nonlinear inequality constraints are investigated. These problems are widely used in many fields such as industry, agriculture, energy, transportation, etc. Therefore, studying on sta-ble and efficient numerical algorithms for inequality constrained optimization has important theoretical and practical significance.In this thesis, we propose two SQP algorithms without a penalty func-tion or a filter for inequality constrained optimization. Firstly, based on the idea of filter method and nonmonotone line search technique, we propose a SQP algorithm without a penalty function or a filter for inequality constrained optimization. The algorithm has the following properties:the initial point is arbitrary; The difficulty of choosing suitable penalty parameter is over-come due to no using penalty function; A filter is not introduced by setting the upper bound of the constraint violation; Under the strict Mangasarian-Fromovitz constraint qualification and other mild conditions, the algorithm possesses global convergence. We report some preliminary numerical results which show the effectiveness of the proposed algorithm.Secondly, based on norm-relaxed technique and nonmonotone line search technique, we propose a norm-relaxed SQP algorithm without a penalty func- tion or a filter for inequality constrained optimization. At each iteration, the search direction is obtained by solving a norm-relaxed quadractic program-ming subproblem. The step size is selected by a nonmonotone line search. The algorithm has the following properties:the norm-relaxed quadractic pro-gramming subproblem has optimal solution; The new reduction of the objec-tive function or constraint violation is used in the nonmonotone line search, which can accelerate the convergence and improve the numerical effect of the algorithm. We also report some preliminary numerical results which show the effectiveness of the proposed algorithm.