| In this master thesis, optimization problems with nonlinear inequal-ity constraints are discussed. Referring to the idea of filter algorithm, we propose a new generalized gradient projection algorithm. This algo-rithm does neither use a penalty function nor adopt a real filter. The initial point of the proposed method is arbitrary. At each iteration, the search direction is yielded just by explicit generalized gradient projection formula. The step-size is selected such that either the value of the ob-jective function or the measure of the constraint violations is sufficiently reduced by a Armijo line search technique.Our algorithm have some main properties as follows:Firstly, we do not require to assume the boundedness of iteration sequence:Secondly, we do not require any restoration phase which is necessary for filter methods; The scale and the computation cost are further decreased by using ε-active set. The algorithm possesses global convergence under the Linear Independence constraint qualification (LICQ) and some suitable assumptions. Finally, some primary numerical results which show that the proposed method is promising. |
