Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems ㅡ Inequality Constrained Problems (Journal of Computational Mathematics, 2002)
In this paper, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints is proposed. Since the new algorithm only needs to solve several systems of linear equations gaving a same coefficient matrix per iteration, the computation amount of the algorithm is much less than that of the existing SQP algorithms per iteration. Moreover, for the SQP type algorithms, there exist so-called inconsistent problems, i.e., quadratic programming subproblems of the SQP algorithms may not have a solution at some iterations, but this phenomenon will not occur with the SSLE algorithms because the related systems of linear equations always have solutions. Some numerical results are reported.
Keywords: Optimization; Inequality constraints; Algorithms; Sequential systems of linear equations; Coefficient matrices; Superlinear convergence.