A QP-Free Algorithm Without A Penalty Function Or A Filter For General Constrained Optimization

A QP-free algorithm without a penalty function or a filter is proposed in this dissertation.Firstly, based on the new techniques of working set and perturbation technique, the new systems of linear equations are constructed. At each it-eration, the proposed algorithm only needs to solve two or three systems of linear equations with the same coefficient matrix to obtain the search direc-tion and high-order correction direction.Secondly, in order to avoid using penalty parameters and filter, we adopt nonmonotone search for the biobjective of the descent of objective function and the feasibility of constraints. The line search technique ensures that the objective function or constraint violation function possesses sufficient de-scent property.The proposed algorithm has the following features:(1)At each iteration, two or three systems of linear equations with the same coefficient matrix are solved. (2) Using new working set technique reduces the size of the systems of equations. Consequently computational cost is further decreased and so as to further reduce the amount of calculation, improve numerical effect; (3) Because neither the penalty function nor filter is used, the difficulties of se- lecting appropriate penalty parameters and the large storage problem of filter are overcomed. (4) There is no feasibility recovery phase, so computational amount is decreased greatly (5) Under appropriate assumptions, the pro-posed algorithm possesses global convergence and superlinear convergence.At the end of this dissertation, some preliminary numerical results are reported. These results show that the proposed algorithm is effective.