tailieunhanh - Báo cáo hóa học: " Research Article A Note on Convergence Analysis of an SQP-Type Method for Nonlinear Semidefinite Programming"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article A Note on Convergence Analysis of an SQP-Type Method for Nonlinear Semidefinite Programming | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 218345 10 pages doi 2008 218345 Research Article A Note on Convergence Analysis of an SQP-Type Method for Nonlinear Semidefinite Programming Yun Wang 1 Shaowu Zhang 2 and Liwei Zhang1 1 Department of Applied Mathematics Dalian University of Technology Dalian 116024 China 2 Department of Computer Science Dalian University of Technology Dalian 116024 China Correspondence should be addressed to Yun Wang wangyun_3412@ Received 29 August 2007 Accepted 23 November 2007 Recommended by Kok Lay Teo We reinvestigate the convergence properties of the SQP-type method for solving nonlinear semidef-inite programming problems studied by Correa and Ramirez 2004 . We prove under the strong second-order sufficient condition with the sigma term that the local SQP-type method is quadrati-cally convergent and the line search SQP-type method is globally convergent. Copyright 2008 Yun Wang et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction We consider the following nonlinear semidefinite programming SDP min f x . h x 0 g x where x R f R R h R RZ and g R Sp are twice continuously differentiable functions Sp is the linear space of all p X p real symmetric matrices and Sp is the cone of all p X p symmetric positive semidefinite matrices. Fares et al. 2002 1 studied robust control problems via sequential semidefinite programming technique. They obtained the local quadratic convergence rate of the proposed SQP-type method and employed a partial augmented Lagrangian method to deal with the problems addressed there. Correa and Ramirez 2004 2 systematically studied an SQP-type method for solving nonlinear SDP problems and analyzed the convergence properties they obtained the global convergence and .