点击次数：
论文类型：期刊论文
发表时间：2014-04-01
发表刊物：TOP
收录刊物：SCIE
卷号：22
期号：1
页面范围：45-79
ISSN号：1134-5764
关键字：Inverse optimization; Second-order cone quadratic programming; Augmented Lagrangian method; Rate of convergence; Damped semismooth Newton method
摘要：The focus of this paper is on studying an inverse second-order cone quadratic programming problem, in which the parameters in the objective function need to be adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with cone constraints, and its dual, which has fewer variables than the original one, is a semismoothly differentiable (SC (1)) convex programming problem with both a linear inequality constraint and a linear second-order cone constraint. We demonstrate the global convergence of the augmented Lagrangian method with an exact solution to the subproblem and prove that the convergence rate of primal iterates, generated by the augmented Lagrangian method, is proportional to 1/r, and the rate of multiplier iterates is proportional to , where r is the penalty parameter in the augmented Lagrangian. Furthermore, a semismooth Newton method with Armijo line search is constructed to solve the subproblems in the augmented Lagrangian approach. Finally, numerical results are reported to show the effectiveness of the augmented Lagrangian method with both an exact solution and an inexact solution to the subproblem for solving the inverse second-order cone quadratic programming problem.