The Polak-Ribière-Polyak conjugate gradient algorithm is a useful tool of unconstrained numerical optimization. Efficient implementations of the algorithm usually perform line searches satisfying the strong Wolfe conditions. It is well known that these conditions do not guarantee that the successive computed directions are descent directions. This paper proposes a relaxation of the strong Wolfe...

In this paper, we propose a modified Polak–Ribière–Polyak (PRP) conjugate gradient method. An attractive property of the proposed method is that the direction generated by the method is always a descent direction for the objective function. This property is independent of the line search used. Moreover, if exact line search is used, the method reduces to the ordinary PRP method. Under appropria...

The BFGS method is one of the most famous quasi-Newton algorithms for unconstrained optimization. In 1984, Powell presented an example of a function of two variables that shows that the Polak–Ribière–Polyak (PRP) conjugate gradient method and the BFGS quasi-Newton method may cycle around eight nonstationary points if each line search picks a local minimum that provides a reduction in the object...

1Department of Gynecology and Obstetrics, Faculty of Medicine, Masaryk University, Brno, Czech Republic, 2Department of Histology and Embryology, Faculty of Medicine, Masaryk University, Brno, Czech Republic, 3Department of Histology and Embryology, Faculty of Medicine, Comenius University, Bratislava, Slovakia, and 4University Centrum of Reproductive Medicine of the 1st Department of Gynecolog...

BACKGROUND A previous study has shown that variations in threshold and intensity (lipid goal attainment) of statins for primary prevention contribute to regional differences in overall consumption of statins in Norway. Our objective was to explore how differences in prevalences of use, dosing characteristics, choice of statin and continuity of therapy in individual patients adds new information...

Providing seamless QoS guarantees for multimedia services is one of the most critical requirements in the mobile Internet. However, the effects of host mobility make it difficult to provide such services. The next steps in signaling (NSIS) was proposed by the IETF as a new signaling protocol, but it fails to address some mobility issues. This paper proposes a new QoS NSIS signaling layer protoc...

The General Internet Signaling Transport (GIST) protocol was specified by the IETF in order to provide a generic transport protocol for signaling messages. A group at the Institute of Telematics implemented the GIST protocol and evaluated it already in smaller testbed setups. An evaluation of GIST in large-scale scenarios can, however, only be accomplished by using a simulation framework. In th...

Resource reservations in the Internet become more and more important with the advent of real-time multimedia services like Voiceover-IP and IPTV. At the same time we see an increasing interest in accessing Internet services by using mobile devices. In this paper we describe how Quality-of-Service guarantees can be achieved in mobile environments across different domains using the Next Steps in ...