@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 = {<p style="text-align: justify;">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 &quot;$σ$-term&quot; 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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/17871.html}
}