This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such problems considered in both exact and inexact forms. Using generalized differential tools of second-order variational analysis, we formulate the corresponding version of second-order sufficiency and use it to establish, among other results, the uniform second-order growth condition for the augmented Lagrangian. The latter allows us to justify the solvability of subproblems in the ALM and to prove the linear primal-dual convergence of this method.

翻译：本文论述在优化理论和应用中重要的二阶锥体编程问题,主要关注的是针对以准确和不确切形式考虑的这类问题的拉格朗日强化法(ALM),利用二阶变异分析的普遍差别工具,我们制定相应的第二阶次充裕性,并用它来确定,除其他结果外,扩大拉格朗日人统一的第二阶次增长条件,后者使我们能够证明ALM子问题的可溶性,并证明这一方法的线性初步趋同。