Volume 17, Issue 4
Superlinear Convergence of an SQP-Type Method for Nonlinear Semidefinite Programming

Int. J. Numer. Anal. Mod., 17 (2020), pp. 592-612.

Published online: 2020-08

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• 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.

• Keywords

Nonlinear semidefinite programming, SQP-type method, second order sufficient condition, constraint nondegeneracy, superlinear convergence.

• AMS Subject Headings

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@Article{IJNAM-17-592, author = {Fu , Wenhao and Chen , Zhongwen}, title = {Superlinear Convergence of an SQP-Type Method for Nonlinear Semidefinite Programming}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17871.html} }
TY - JOUR T1 - Superlinear Convergence of an SQP-Type Method for Nonlinear Semidefinite Programming AU - Fu , Wenhao AU - Chen , Zhongwen JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 592 EP - 612 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17871.html KW - Nonlinear semidefinite programming, SQP-type method, second order sufficient condition, constraint nondegeneracy, superlinear convergence. AB -

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.

Wenhao Fu & Zhongwen Chen. (2020). Superlinear Convergence of an SQP-Type Method for Nonlinear Semidefinite Programming. International Journal of Numerical Analysis and Modeling. 17 (4). 592-612. doi:
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