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A sensitivity result for quadratic second-order cone programming and its application
Applications of Mathematics, Tome 66 (2021) no. 3, pp. 413-436 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2020.0278-19
Classification : 90C20, 90C22, 90C31
Keywords: sensitivity; quadratic second-order cone programming; nonlinear second-order cone programming; local convergence 
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Zhao, Qi; Fu, Wenhao; Chen, Zhongwen. A sensitivity result for quadratic second-order cone programming and its application. Applications of Mathematics, Tome 66 (2021) no. 3, pp. 413-436. doi: 10.21136/AM.2020.0278-19

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