SEQUENTIAL SYSTEMS OF LINEAR-EQUATIONS ALGORITHM FOR NONLINEAR OPTIMIZATION PROBLEMS WITH GENERAL CONSTRAINTS

In Ref. 1, a new superlinearly convergent algorithm of sequential syst ems of linear equations (SSLE) for nonlinear optimization problems wit h inequality constraints was proposed. At each iteration, this new alg orithm only needs to solve four systems of linear equations having the same coefficient matrix, which is much less than the amount of comput ation required for existing SQP algorithms. Moreover, unlike the quadr atic programming subproblems of the SQP algorithms (which may not have a solution), the subproblems of the SSLE algorithm are always solvabl e. In Ref. 2, it is shown that the new algorithm can also be used to d eal with nonlinear optimization problems having both equality and ineq uality constraints, by solving an auxiliary problem. But the algorithm of Ref 2 has to perform a pivoting operation to adjust the penalty pa rameter per iteration. In this paper, we improve the work of Ref 2 and present a new algorithm of sequential systems of linear equations for general nonlinear optimization problems. This new algorithm preserves the advantages of the SSLE algorithms, while at the same time overcom ing the aforementioned shortcomings. Some numerical results are also r eported.