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 - <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>