Alternating direction method of multipliers for the extended trust region subproblem

Iranian Journal of Numerical Analysis and Optimization

مقاله 5، دوره 7، شماره 1 - شماره پیاپی 11، تیر 2017، صفحه 107-117   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v7i1.52283

نویسندگان

M. Salahi^* ؛ A. Taati

Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

چکیده

The extended trust region subproblem has been the focus of several research recently. Under various assumptions, strong duality and certain SOCP/SDP relaxations have been proposed for several classes of it. Due to its importance, in this paper, without any assumption on the problem, we apply the widely used alternating direction method of multipliers (ADMM) to solve it. The convergence of ADMM iterations to the first order stationary conditions is established. On several classes of test problems, the quality of the solution obtained by the ADMM for medium scale problems is compared with the SOCP/SDP relaxation. Moreover, the applicability of the method for solving large scale problems is shown by solving several large instances.

کلیدواژه‌ها

Extended trust region subporblem؛ Alternating method؛ Nonconvex optimization؛ Semidefinite program؛ Second order cone program

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