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...

Sparse reconstruction inspired by compressed sensing has attracted considerable attention in fluorescence molecular tomography (FMT). However, the columns of system matrix used for FMT reconstruction tend to be highly coherent, which means L1 minimization may not produce the sparsest solution. In this paper, we propose a novel reconstruction method by minimization of the difference of L1 and L2...

in this paper the optimal control of boundary heat flux in a 2-d solid body with an arbitrary shape is performed in order to achieve the desired temperature distribution at a given time interval. the boundary of the body is subdivided into a number of components. on each component a time-dependent heat flux is applied which is independent of the others. since the thermophysical properties are t...

Correspondence: Catherine Powell, School of Nursing and Midwifery, University of Southampton, Nightingale Building (67), Highfield, Southampton SO17 1BJ, UK. E-mail: [email protected] POWELL C. (2003) Journal of Advanced Nursing 41(4), 376–382 The Delphi technique: myths and realities Aim. To outline the key concepts and principles of the Delphi technique. Methods. Reference is made to a selectio...