Mathematics – Optimization and Control
Scientific paper
2011-09-15
Mathematics
Optimization and Control
37 pages, 3 figures
Scientific paper
In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature, we allow one to solve the primal problem inexactly up to a given accuracy. The inexact perturbed algorithm allows to use both approximate Hessian matrices and approximate gradient vectors to compute Newton-type directions for the dual problem. The algorithm is divided into two phases. The first phase computes an initial point which makes use of inexact perturbed damped Newton-type iterations, while the second one performs the path-following algorithm with inexact perturbed full-step Newton-type iterations. We analyze the convergence of both phases and estimate the worst-case complexity. As a special case, an exact path- following algorithm for Lagrangian relaxation is derived and its worst-case complexity is estimated. This variant possesses some differences compared to the previously known methods. Implementation details are discussed and numerical results are reported.
Diehl Moritz
Dinh Quoc Tran
Necoara Ion
Savorgnan Carlo
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