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Reviewed by Hiroshi Yabe

By Xinwei (prc-hbt-am) Yuan and Ya Xiang (prc-asbj-enm


A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties. (English summary) Math. Program. 125 (2010), no. 1, Ser. A, 163–193. Types of primal-dual interior-point methods for nonlinearly constrained optimization problems include those with a line search procedure, a trust region strategy or a filter technique. In this paper, the authors propose a null-space primal-dual interior-point method which computes a range-space step and a null-space step to solve an equality constrained barrier subproblem and which uses an l2 penalty merit function within the framework of a line search strategy. The method is related to that of X.-W. Liu and J. Sun [SIAM J. Optim. 14 (2004), no. 4, 1163–1186; MR2112969 (2005j:90098)]. Under mild assumptions, it is proved that either every limit point of the iterates is a KKT point of the barrier subproblem, or there exists a limit point that is either an infeasible stationary point of minimizing the l2 norm of violations of the constraints of the original problem or a Fritz John point of the original problem. Furthermore, the superlinear and/or quadratic convergence of the algorithm is analyzed

Year: 2013
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