A Simple Alternating Direction Method for the Conic Trust Region Subproblem
نویسندگان
چکیده
منابع مشابه
alternating direction method of multipliers for the extended trust region subproblem
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 ...
متن کاملan adaptive nonmonotone trust region method for unconstrained optimization problems based on a simple subproblem
using a simple quadratic model in the trust region subproblem, a new adaptive nonmonotone trust region method is proposed for solving unconstrained optimization problems. in our method, based on a slight modification of the proposed approach in (j. optim. theory appl. 158(2):626-635, 2013), a new scalar approximation of the hessian at the current point is provided. our new proposed method is eq...
متن کاملThe generalized trust region subproblem
The interval bounded generalized trust region subproblem (GTRS) consists in minimizing a general quadratic objective, q0(x) → min, subject to an upper and lower bounded general quadratic constraint, l ≤ q1(x) ≤ u. This means that there are no definiteness assumptions on either quadratic function. We first study characterizations of optimality for this implicitly convex problem under a constrain...
متن کاملSolving the Trust-Region Subproblem using the Lanczos Method
The approximate minimization of a quadratic function within an ellipsoidal trust region is an important subproblem for many nonlinear programming methods. When the number of variables is large, the most widely-used strategy is to trace the path of conjugate gradient iterates either to convergence or until it reaches the trust-region boundary. In this paper, we investigate ways of continuing the...
متن کاملOn SOCP/SDP Formulation of the Extended Trust Region Subproblem
We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2018
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2018/5358191