On SOCP/SDP Formulation of the Extended Trust Region Subproblem

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...

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 ...

Regularization 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...

A Survey of the Trust Region Subproblem within aSemide nite

Polynomial Solvability of Variants of the Trust-Region Subproblem

We consider an optimization problem of the form min xQx+ cx s.t. ‖x− μh‖ ≤ rh, h ∈ S, ‖x− μh‖ ≥ rh, h ∈ K, x ∈ P, where P ⊆ R is a polyhedron defined by m inequalities and Q is general and the μh ∈ R and the rh quantities are given; a strongly NP-hard problem. In the case |S| = 1, |K| = 0 and m = 0 one obtains the classical trust-region subproblem which is polynomially solvable, and has been th...

Solving 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...