Year: 2020
Author: Wenhao Fu, Zhongwen Chen
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 4 : pp. 592–612
Abstract
In this paper, we study the rate of convergence of a sequential quadratic programming (SQP) method for nonlinear semidefinite programming (SDP) problems. Since the linear SDP constraints does not contribute to the Hessian of the Lagrangian, we propose a reduced SQP-type method, which solves an equivalent and reduced type of the nonlinear SDP problem near the optimal point. For the reduced SDP problem, the well-known and often mentioned "$σ$-term" in the second order sufficient condition vanishes. We analyze the rate of local convergence of the reduced SQP-type method and give a sufficient and necessary condition for its superlinear convergence. Furthermore, we give a sufficient and necessary condition for superlinear convergence of the SQP-type method under the nondegeneracy condition, the second-order sufficient condition with $σ$-term and the strict complementarity condition.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-IJNAM-17871
International Journal of Numerical Analysis and Modeling, Vol. 17 (2020), Iss. 4 : pp. 592–612
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Nonlinear semidefinite programming SQP-type method second order sufficient condition constraint nondegeneracy superlinear convergence.