A new noninterior continuation method for solving a system of equalities and inequalities

By using slack variables and minimum function,we first reformulate the system of equalities and inequalities as a system of nonsmooth equations,and,using smoothing technique,we construct the smooth operator. a new noninterior continuation method is proposed to solve the system of smooth equations. it shows that any accumulation point of the iteration sequence generated by our algorithm is a solution of the system of equalities and inequalities. some numerical experiments show the feasibility and efficiency of the algorithm. © 2014 jianguang zhu and binbin hao.