Traversing non-convex regions

This paper considers a method for dealing with non-convex objective functions in optimization problems. It uses the Hessian matrix and combines features of trust-region techniques and continuous steepest descent trajectory-following in order to construct an algorithm which performs curvilinear searches away from the starting point of each iteration. A prototype implementation yields promising resultsPeer reviewe

Dimethyl fumarate in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Dimethyl fumarate (DMF) inhibits inflammasome-mediated inflammation and has been proposed as a treatment for patients hospitalised with COVID-19. This randomised, controlled, open-label platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing multiple treatments in patients hospitalised for COVID-19 (NCT04381936, ISRCTN50189673). In this assessment of DMF performed at 27 UK hospitals, adults were randomly allocated (1:1) to either usual standard of care alone or usual standard of care plus DMF. The primary outcome was clinical status on day 5 measured on a seven-point ordinal scale. Secondary outcomes were time to sustained improvement in clinical status, time to discharge, day 5 peripheral blood oxygenation, day 5 C-reactive protein, and improvement in day 10 clinical status. Between 2 March 2021 and 18 November 2021, 713 patients were enroled in the DMF evaluation, of whom 356 were randomly allocated to receive usual care plus DMF, and 357 to usual care alone. 95% of patients received corticosteroids as part of routine care. There was no evidence of a beneficial effect of DMF on clinical status at day 5 (common odds ratio of unfavourable outcome 1.12; 95% CI 0.86-1.47; p = 0.40). There was no significant effect of DMF on any secondary outcome

Optimizing Preventive Maintenance Models

' The original publication is available at www.springerlink.com ' Copyright SpringerWe deal with the problem of scheduling preventive maintenance (PM) for a system so that, over its operating life, we minimize a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that a hazard rate model is known which predicts the frequency of system failure as a function of age. It is also assumed that each PM produces a step reduction in the effective age of the system. We consider some variations and extensions of a PMscheduling approach proposed by Lin et al [6]. In particular we consider numerical algorithms which may be more appropriate for hazard rate models which are less simple than those used in [6] and we introduce some constraints into the problem in order to avoid the possibility of spurious solutions. We also discuss the use of automatic differentiation (AD) as a convenient tool for computing the gradients and Hessians that are needed by numerical optimization methods. The main contribution of the paper is a new problem formulation which allows the optimal number of occurrences of PM to be determined along with their optimal timings. This formulation involves the global minimization of a non-smooth performance function. In our numerical tests this is done via the algorithm DIRECT proposed by Jones et al [19]. We show results for a number of examples, involving different hazard rate models, to give an indication of how PM schedules can vary in response to changes in relative costs of maintenance, repair and replacement.Peer reviewe

Nonlinear Optimization with Financial Applications

The book introduces the key ideas behind practical nonlinear optimization. Computational finance - an increasingly popular area of mathematics degree programs - is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material - which occupies about one-third of the text - is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performa

Modelling and Optimizing Sequential Imperfect Preventive Maintenance

Original article can be found at: http://www.sciencedirect.com/science/journal/09518320 Copyright Elsevier Ltd. DOI: 10.1016/j.ress.2008.03.002Peer reviewe

A self-stabilizing Pantoja-like indirect algorithm for optimal control

Original article can be found at: http://www.informaworld.com/smpp/title~content=t713645924 Copyright Taylor and Francis / Informa.In 1983 Pantoja described a computationally efficient stagewise construction of the Newton direction for the discrete time optimal control problem. Automatic Differentiation can be used to implement Pantoja's algorithm and calculate the Newton direction, without truncation error, and without extensive manual re-writing of targetfunction code to form derivatives. Pantoja's algorithm is direct, in that the independent variables are the control vectors at each timestep. In this paper we formulate an indirect analogue of Pantoja's algorithm, in which the only independent variables are the components of a costate vector corresponding to the initial timestep. This reformulated algorithm gives exactly the Newton step for the initial costate with respect to a terminal transversality condition: at each timestep we solve implicit equations for the current controlsand successor costates. A remarkable feature of the indirect algorithm is that it is straiehtforward to comensate for the effect of non-zero residuals in the implicit costate equations. .The indirect reformulation of Pantoja's algorithm set out in this paper is a suitable basis for verified optimization using interval methods.Peer reviewe

Global Convergence of a Curvilinear Search for Non-Convex Optimization

© 2022 Springer. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/s11075-022-01375-yFor a non-convex function f : R^n → R with gradient g and Hessian H, define a step vector p(μ,x) as a function of scalar parameter μ and position vector x by the equation (H(x) + μI)p(μ, x) = −g(x). Under mild conditions on f, we construct criteria for selecting μ so as to ensure that the algorithm x := x + p(μ, x) descends to a second order stationary point of f, and avoids saddle points.Peer reviewe

Application of global optimisation to particle identification using light scattering

‘In these times, during the rise in the popularity of institutional repositories, the Society does not forbid authors from depositing their work in such repositories. However, the AAS regards the deposit of scholarly work in such repositories to be a decision of the individual scholar, as long as the individual's actions respect the diligence of the journals and their reviewers.’ Original article can be found at : http://iopscience.iop.org/ Copyright American Astronomical SocietyNumerical methods of solving the inverse light scattering problem for spheres are presented. The methods are based on two stochastic global optimization techniques: Deep's random search and the multilevel single-linkage clustering analysis due to Rinnooy Kan and Timmer. Computational examples show that the radius and the refractive index of spheres comparable with or larger than the wavelength of light can be recovered from multiangle scattering data. While the random search approach is faster, the clustering analysis is shown to be more reliable. A general discussion of the clustering method is also given.Peer reviewe