Yuying Li

An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds

There are provided pressed spherical fuel elements for high temperature reactors made of a graphite matrix with separate embedded coated fuel and fertile material particles wherein the fuel elements comprise 3 concentric layers including a graphite nucleus or core (1) which only contains fertile material particles (4), this graphite nucleus (1) is surrounded by a graphite zone (2) which only contains the fuel particles (5) and this is encased in a shell (3) of pure graphite, the same graphite material being present in all three layers.

A computational algorithm for minimizing total variation in image restoration

A reliable and efficient computational algorithm for restoring blurred and noisy images is proposed. The restoration process is based on the minimal total variation principle introduced by Rudin et al. For discrete images, the proposed algorithm minimizes a piecewise linear l (1) function (a measure of total variation) subject to a single 2-norm inequality constraint (a measure of data fit). The algorithm starts by finding a feasible point for the inequality constraint using a (partial) conjugate gradient method. This corresponds to a deblurring process. Noise and other artifacts are removed by a subsequent total variation minimization process. The use of the linear l(1) objective function for the total variation measurement leads to a simpler computational algorithm. Both the steepest descent and an affine scaling Newton method are considered to solve this constrained piecewise linear l(1) minimization problem. The resulting algorithm, when viewed as an image restoration and enhancement process, has the feature that it can be used in an adaptive/interactive manner in situations when knowledge of the noise variance is either unavailable or unreliable. Numerical examples are presented to demonstrate the effectiveness of the proposed iterative image restoration and enhancement process.

A Globally Convergent Method for

The

l_p

l_p

Problems

-norm discrete estimation problem

Primal methods are better than dual methods for solving overdetermined linear systems in the l ∞ sense?

min_{x in Re^n } ||b - A^T x||_p^p

A Structure-Exploiting Algorithm for Nonlinear Minimax Problems

is troublesome when p is close to unity because the objective function approaches a nonsmooth form as p converges to one. This paper presents an efficient algorithm for solving

Piecewise Differentiable Minimization for Ill-posed Inverse Problems

l_p

On the Convergence of Reflective Newton Methods for Large-scale Nonlinear Minimization Subject to Bounds

-norm problems for all

Large-scale numerical optimization

1 leq p < 2