We describe an approach to managing the use of approximate models in optimization. This approach combines the idea of approximation models from engineering design optimization with the model trust region approach from nonlinear programming. The trust region framework regulates the amount of optimization done with the approximate models before one needs to appeal to a detailed model to check the...

We present a new method for large-scale nonnegative regularization, based on a quadratically and nonnegatively constrained quadratic problem. Such problems arise for example in the regularization of ill-posed problems in image restoration where, in addition, some of the matrices involved are very ill-conditioned. The method is an interior-point iteration that requires the solution of a large-sc...

An attempt is made to interpret the various existing experimental data on the single spin asymmetries in inclusive pion production by the polarized proton and antiproton beams. As the basis of analysis the chromo-magnetic string model is used. A whole measured kinematic region is covered. The successes and fails of such approach are outlined. The possible improvements of model are discussed.

The trust{region subproblem arises frequently in linear algebra and optimization applications. Recently, matrix{free methods have been introduced to solve large{ scale trust{region subproblems. These methods only require a matrix{vector product and do not rely on matrix factorizations 4, 7]. These approaches recast the trust{ region subproblem in terms of a parameterized eigenvalue problem and ...

In this paper we study the global convergence behavior of a class of composite–step trust–region SQP methods that allow inexact problem information. The inexact problem information can result from iterative linear systems solves within the trust–region SQP method or from approximations of first–order derivatives. Accuracy requirements in our trust– region SQP methods are adjusted based on feasi...

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...