The trust-region subproblem of minimizing a quadratic function subject to a norm constraint arises in the context of trust-region methods in optimization and in the regularization of discrete forms of ill-posed problems, including non-negative regularization by means of interior-point methods. A class of efficient methods and software for solving large-scale trust-region subproblems is based on...

In this paper we present a method of parameter optimization, relative trust-region learning, where the trust-region method and the relative optimization [21] are jointly exploited. The relative trust-region method finds a direction and a step size with the help of a quadratic model of the objective function (as in the conventional trust-region methods) and updates parameters in a multiplicative...

We present in this paper a class of trust region algorithms in which the structure of the problem is explicitly used in the very denition of the trust region itself. This development is intended to re BLOCKINect the possibility that some parts of the problem may be more \trusted" than others, a commonly occurring situation in large-scale nonlinear applications. After describing the structured t...

We consider the problem of coarsely managed multiple access wideband systems, where each user can control its own transmission power and rate, independent of other users’ actions, according to the policy specified by central controlling agent: base station. Even with such coarse coordination, multiuser detection enables a system superior to any orthogonal division system like TDMA. We fully cha...

Computing a few eigenpairs of large-scale matrices is a significant problem in science and engineering applications and a very active area of research. In this paper, two methods that compute extreme eigenpairs of positive-definite matrix pencils are combined into a hybrid scheme that inherits the advantages of both constituents. The hybrid algorithm is developed and analyzed in the framework o...

Experimental measurements of angular correlations in three-jet final states have recently been performed in DIS. Next-to-leading-order QCD results for these observables are affected by large theoretical uncertainties in the kinematic region of the data. We discuss the effects of multiple QCD radiation at higher order using parton-shower methods based on transverse-momentum dependent parton dist...

We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraintdefining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Numerical experiments...

A trust-region-based BFGS method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the linesearch technique will be used instead of repeatedly solving the subproblem of the normal trust-region method. We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given ...

In this paper, we present a class of trust region algorithms for minimization problems within convex feasible regions, in which the structure of the problem is explicitly used in the deenition of the trust region. This development is intended to reeect the possibility that some parts of the problem may be more accurately modelled than others, a common occurrence in large-scale nonlinear applica...