A Norm-Relaxed Method With Identification Function For General Constrained Optimization

In this paper, based on a semi-penalty function and an identification function, as well as the norm-relaxed method, we discuss a kind of optimization problem with nonlinear equality and inequality constraints. First, with the help of semi-penalty function, we translate the general constrained problem into an auxiliary problem with only inequality constraints, then using the information in updating the penalty parameter, a simple form of "working set" is derived. Finally, combining the technique of working set with norm-relaxed method, a new norm-relaxed algorithm is presented. At each iteration, due to using the technique of working set, only one reduced QP subproblem and one reduced system of linear equation will be solved to yield the search direction and the high-order correction direction respectively, the scale and cost of computation is further reduced. The algorithm possesses global convergence and superlinear convergence under some mild assumptions without the strict complementarity.The main features of the algorithm can be summarized as follows·the parameter is adjusted automatically only finite number of times;·the working set is simple;·the cost of computation is reduced by using the technique of working set;·an improved direction is obtained by solving only one subproblem;·global convergence and superlinear convergence are obtained under some suitable assumptions without strict complementarity.Finally, some preliminary numerical results show that the proposed algorithm is promising.