Abstract: In this paper, based on a semi-penalty function and　an identification function used to yield a  ``working set'', as well as the norm-relaxed SQP idea, a new
algorithm for solving a kind of optimization problems with nonlinear　equality and inequality constraints is proposed. At each iteration,　to yield the search directions the algorithm solves only one reduced quadratic program (QP) subproblem and a reduced system of linear equations. The proposed algorithm possesses global convergence and superlinear convergence under some mild assumptions without the strictly complementarity. Finally, some elementary numerical experiments are reported.

Key words: integral tree, characteristic polynomial, diophantine equation, graph spectrum