A sequential quadratically constrained quadratic programming method with an augmented Lagrangian line search function

Authors:
Chun-Ming Tang;Jin-Bao Jian
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, PR China and College of Mathematics and Information Science, Guangxi University, Nanning, PR China;College of Mathematics and Information Science, Guangxi University, Nanning, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The ''active set'' strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered.