This paper focuses on a class of second-order cone programming problems with linear constraints. Based on the indicator function on second-order cones, we reformulate the second-order cone program as an optimization problem with a nonsmooth objective function and linear constraints. We establish the KL property for the augmented Lagrangian functions of the reformulated problem and deduce the KL exponent is at the critical point under the strict constraint qualification and second-order sufficient condition.

second-order cone programming, the augmented Lagrangian function, KL property, KL exponent.

Received: November 8, 2022; Accepted: December 27, 2022; Published: January 12, 2023

How to cite this article: Yi Zhang and Mengqi Mao, The KL exponent for the augmented Lagrangian function of second-order cone programming with linear constraints, Far East Journal of Applied Mathematics 116(1) (2023), 35-45. http://dx.doi.org/10.17654/0972096023002

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