On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization  

作　　者：Yong Gang PEI De Tong ZHU 

机构地区：[1]Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College o] Mathematics and Information Science, He 'nan Normal University, Xinxiang 453007, P. R. China [2]Mathematics and Science College, Shanghai Normal University, Shanghai 200234, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2018年第12期1804-1828,共25页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.11671122 and 11371253);Key Scientific Research Project for Colleges and Universities in He’nan Province(Grant No.15A110031);Key Scientific and Technological Project of He’nan Province(Grant No.162102210069);Natural Science Foundation of He’nan Normal University(Grant No.2014QK04);Ph.D. Research Foundation of He’nan Normal University(Grant Nos.QD13041 and QD14155)

摘　　要：A trust-region sequential quadratic programming （SQP） method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the trans- position of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported.A trust-region sequential quadratic programming （SQP） method is developed and analyzed for the solution of smooth equality constrained optimization problems. The trust-region SQP algorithm is based on filter line search technique and a composite-step approach, which decomposes the overall step as sum of a vertical step and a horizontal step. The algorithm includes critical modifications of horizontal step computation. One orthogonal projective matrix of the Jacobian of constraint functions is employed in trust-region subproblems. The orthogonal projection gives the null space of the trans- position of the Jacobian of the constraint function. Theoretical analysis shows that the new algorithm retains the global convergence to the first-order critical points under rather general conditions. The preliminary numerical results are reported.

关 键 词：Sequential quadratic programming TRUST-REGION filter line search PROJECTION global convergence 

分 类 号：O224[理学—运筹学与控制论] TP301.6[理学—数学]