A Fast Eigenvalue Approach for Solving the Trust Region Subproblem with an Additional Linear Inequality
نویسنده
چکیده
In this paper, we study the extended trust region subproblem (eTRS) in which the trust region intersects the unit ball with a single linear inequality constraint. By reformulating the Lagrangian dual of eTRS as a two-parameter linear eigenvalue problem, we state a necessary and sufficient condition for its strong duality in terms of an optimal solution of a linearly constrained bivariate concave maximization problem. This results in an efficient algorithm for solving eTRS of large size whenever the strong duality is detected. Finally, some numerical experiments are given to show the effectiveness of the proposed method.
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Trust region subproblem (TRS), which is the problem of minimizing a quadratic function over a ball, plays a key role in solving unconstrained nonlinear optimization problems. Though TRS is not necessarily convex, there are efficient algorithms to solve it, particularly in large scale. Recently, extensions of TRS with extra linear constraints have received attention of several researchers. It ha...
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