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On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization
Authors:Yong Gang Pei  De Tong Zhu
Institution:1. Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of 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
Abstract: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 transposition 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.
Keywords:Sequential quadratic programming  trust-region  filter line search  projection  global convergence  
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