Based on an eigenvalue analysis, a new proof for the sufficient descent property of the modified Polak-Ribiere-Polyak conjugate gradient method proposed by Yu et al. is presented.

In this work, applying a lemma due to Nunokawa et al. (J. Ineq. Appl. 2015. 1 (2015)  7), we obtain some sufficient inequalities for some certain subclasses of univalent functions.

The challenge of mobilizing knowledge to improve patient care, population health and ensure effective use of resources is an enduring one in healthcare systems across the world. This commentary reflects on an earlier paper by Ferlie and colleagues that proposes the resource-based view (RBV) of the firm as a useful theoretical lens through which to study knowledge mobilization in healthcare. Specifically, the commentary considers 3 areas that need to be addressed in relation to the proposed application of RBV: the definition of competitive advantage in healthcare; the contribution of macro level theory to understanding knowledge mobilization in healthcare; and the need to embrace and align multiple theories at the micro, meso, and macro levels of implementation.

In this paper, we present a new hybrid conjugate gradient method for unconstrained optimization that possesses sufficient descent property independent of any line search. In our method, a convex combination of the Hestenes-Stiefel (HS) and the Fletcher-Reeves (FR) methods, is used as the conjugate parameter and the hybridization parameter is determined by minimizing the distance between the hybrid conjugate gradient direction and direction of the three-term HS method proposed by M. Li (\emph{A family of three-term nonlinear conjugate gradient methods close to the memoryless BFGS method,} Optim. Lett. \textbf{12} (8) (2018) 1911--1927). Under some standard assumptions, the global convergence property on general functions is established. Numerical results on some test problems in the CUTEst library illustrate the efficiency and robustness of our proposed method in practice.

This paper considers the problem of stabilizing a class of linear time-invariant large-scale systems composed of a number of subsystems using several local dynamic output feedback controllers. For this problem, a sufficient condition on each closed-loop individual subsystem is derived under which the decentralized controller composed of the local controllers designed for individual subsystems, achieves stability for the overall system. This condition is used to convert the decentralized stabilization problem to a set of the H∞ disturbance rejection subproblems.

It is known that the condition Re {zf′ (z)=f (z)}>0, |z|<1 is a sufficient condition for f, f (0) =f′ (0)-1=0 to be starlike in |z|<1. The purpose of this work is to present some new sufficient conditions for univalence and starlikeness.