A Filter-free Sequential Quadratic Programming Algorithm With Infeasibility Detection

Nonlinear programming problems arise from various regions such as na-tional defence,economy,engineering and management.It is very important to develop methods with high efficiency for solving nonlinear constrained programming problems.Sequential quadratic programming(SQP)meth-ods are known to be superlinearly convergent under suitable assumptions and are very popular in solving nonlinear constrained programming prob-lems.A filter-free SQP method is presented for nonlinear inequality con-strained optimization.The method computes a search direction by solving subproblems based on an exact penalty function and has the importan-t feature of infeasibility detection when it is employed to solve infeasible instances.Furthermore,in each iteration,the step is selected such that ei-ther the value of objective function or the measure of constraint violations is sufficiently reduced.A nonmonotone technique originated from the so-lution of unconstraint optimization is applied to accelerate the algorithm.Under standard assumptions,global convergence of the proposed algorith-m is established.The preliminary numerical results are also presented to show the efficiency of the proposed algorithm.