منابع مشابه
The 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 By a Generalized Eigenvalue Problem
The state-of-the-art algorithms for solving the trust-region subproblem are based on an iterative process, involving solutions of many linear systems, eigenvalue problems, subspace optimization, or line search steps. A relatively underappreciated fact, due to Gander, Golub and von Matt in 1989, is that trust-region subproblems can be solved by one generalized eigenvalue problem, with no outer i...
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 کاملRegularization using a parameterized trust region subproblem
We present a new method for regularization of ill-conditioned problems, such as those that arise in image restoration or mathematical processing of medical data. The method extends the traditional trust-region subproblem, TRS, approach that makes use of the L-curve maximum curvature criterion, a strategy recently proposed to find a good regularization parameter. We apply a parameterized trust r...
متن کاملSOCP Reformulation for the Generalized Trust Region Subproblem via a Canonical Form of Two Symmetric Matrices
We investigate in this paper the generalized trust region subproblem (GTRS) of minimizing a general quadratic objective function subject to a general quadratic inequality constraint. By applying a simultaneous block diagonalization approach, we obtain a congruent canonical form for the symmetric matrices in both the objective and constraint functions. By exploiting the block separability of the...
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ژورنال
عنوان ژورنال: Computational Optimization and Applications
سال: 2014
ISSN: 0926-6003,1573-2894
DOI: 10.1007/s10589-013-9635-7