Applications of Mathematics, first online, pp. 1-24


A sensitivity result for quadratic second-order cone programming and its application

Qi Zhao, Wenhao Fu, Zhongwen Chen

Received October 19, 2019.   Published online December 14, 2020.

Abstract:  In this paper, we present a sensitivity result for quadratic second-order cone programming under the weak form of second-order sufficient condition. Based on this result, we analyze the local convergence of an SQP-type method for nonlinear second-order cone programming. The subproblems of this method at each iteration are quadratic second-order cone programming problems. Compared with the local convergence analysis done before, we do not need the assumption that the Hessian matrix of the Lagrangian function is positive definite. Besides, the iteration sequence which is proved to be superlinearly convergent does not contain the Lagrangian multiplier.
Keywords:  sensitivity; quadratic second-order cone programming; nonlinear second-order cone programming; local convergence
Classification MSC:  90C22, 90C31, 90C20
DOI:  10.21136/AM.2020.0278-19

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Affiliations:   Qi Zhao, Jiangsu University of Science and Technology, Zhenjiang, 212001, P.R. China, e-mail: johnzqzq@163.com; Wenhao Fu, School of Mathematical Sciences, Soochow University, Suzhou, 215006, P.R. China, e-mail: wenhfu@163.com; Zhongwen Chen (corresponding author), School of Mathematical Sciences, Soochow University, Suzhou, 215006, P.R. China, e-mail: zwchen@suda.edu.cn


 
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