martin powell makes the point that the death of the national health service (nhs) is constantly asserted without criteria. this article suggests that the nhs is many things, which makes criteria unstable. the alignment of interests in the structure of the nhs enables both overheated rhetoric and political strength, and that pluralization of provision might actually undermine that alignment over...

The quasi-static problem of elastoplasticity with isotropic hardening is considered, with particular emphasis on its numerical solution by means of a Newton-like method. The smoothness properties necessary for such method can be ensured by Moreau-Yosida’s theorem. After time discretization, the classical formulation of the elastoplastic problem is transformed to a minimization problem. The conv...

Recently, Al-Baali (2014) has extended the damped-technique in the modified BFGS method of Powell (1978) for Lagrange constrained optimization functions to the Broyden family of quasi-Newton methods for unconstrained optimization. Appropriate choices for the damped-parameter, which maintain the global and superlinear convergence property of these methods on convex functions and correct the Hess...

A new rank-two variable-metric method is derived using Greenstadt's variational approach [Math. Comp., this issue]. Like the Davidon-Fletcher-Powell (DFP) variable-metric method, the new method preserves the positive-definiteness of the approximating matrix. Together with Greenstadt's method, the new method gives rise to a one-parameter family of variable-metric methods that includes the DFP an...

We present an optimal gradient method for smooth strongly convex optimization. The is in the sense that its worst-case bound on distance to point exactly matches lower oracle complexity class of problems, meaning no black-box first-order can have a better guarantee without further assumptions problems at hand. In addition, we provide constructive recipe obtaining algorithmic parameters and illu...

In combinatorial solution spaces Iterated Local Search (ILS) turns out to be exceptionally successful. The question arises: is ILS also capable of improving the optimization process in continuous solution spaces? To demonstrate that hybridization leads to powerful techniques in continuous domains, we introduce a hybrid meta-heuristic that integrates Powell’s direct search method. It combines di...

We examine various methods for data clustering and data classification that are based on the minimization of the so-called cluster function and its modifications. These functions are nonsmooth and nonconvex. We use Discrete Gradient methods for their local minimization. We consider also a combination of this method with the cutting angle method for global minimization. We present and discuss re...

We consider the linearly constrained `1-`2 minimization and propose the accelerated Bregman method for solving this minimization problem. The proposed method is based on the extrapolation technique, which is used in accelerated proximal gradient methods studied by Nesterov, Nemirovski, and others, and the equivalence between the Bregman method and the augmented Lagrangian method. O( 1 k2 ) conv...