Non-smooth optimization methods for computation of the conditional value-at-risk and portfolio optimization

We examine numerical performance of various methods of calculation of the Conditional Value-at-risk (CVaR), and portfolio optimization with respect to this risk measure. We concentrate on the method proposed by Rockafellar and Uryasev in (Rockafellar, R.T. and Uryasev, S., 2000, Optimization of conditional value-at-risk. Journal of Risk, 2, 21-41), which converts this problem to that of convex optimization. We compare the use of linear programming techniques against a non-smooth optimization method of the discrete gradient, and establish the supremacy of the latter. We show that non-smooth optimization can be used efficiently for large portfolio optimization, and also examine parallel execution of this method on computer clusters.

Chemical structure based prediction of PAN and oxidized PAN fiber density through a non-linear mathematical model

The production of carbon fiber, particularly the oxidation/stabilization step, is a complex process. In the present study, a non-linear mathematical model has been developed for the prediction of density of polyacrylonitrile (PAN) and oxidized PAN fiber (OPF), as a key physical property for various applications, such as energy and material optimization, modeling, and design of the stabilization process. The model is based on the available functional groups in PAN and OPF. Expected functional groups, including [Formula presented], [Formula presented], –CH2, [Formula presented], and [Formula presented], were identified and quantified through the full deconvolution analysis of Fourier transform infrared attenuated total reflectance (FT-IR ATR) spectra obtained from fibers. These functional groups form the basis of three stabilization rendering parameters, representing the cyclization, dehydrogenation and oxidation reactions that occur during PAN stabilization, and are used as the independent variables of the non-linear predictive model. The k-fold cross validation approach, with k = 10, has been employed to find the coefficients of the model. This model estimates the density of PAN and OPF independent of operational parameters and can be expanded to all operational parameters. Statistical analysis revealed good agreement between the governing model and experiments. The maximum relative error was less than 1% for the present model.

Linear optimization for ecological indices based on aggregation functions

We consider an optimization problem in ecology where our objective is to maximize biodiversity with respect to different land-use allocations. As it turns out, the main problem can be framed as learning the weights of a weighted arithmetic mean where the objective is the geometric mean of its outputs. We propose methods for approximating solutions to this and similar problems, which are non-linear by nature, using linear and bilevel techniques.

Mechanical behavior of irregular fibers part II : non-linear tensile behavior

To further our study of the linear tensile behavior of irregular fibers, in this paper we examine the nonlinear tensile behavior of irregular fibers. As before, we simulate the fiber dimensional irregularities with sine waves of different magnitude and frequency, and report results on the tensile behavior and gauge length effect of the simulated fibers.

Parallelization of the discrete gradient method of non-smooth optimization and its applications

We investigate parallelization and performance of the discrete gradient method of nonsmooth optimization. This derivative free method is shown to be an effective optimization tool, able to skip many shallow local minima of nonconvex nondifferentiable objective functions. Although this is a sequential iterative method, we were able to parallelize critical steps of the algorithm, and this lead to a significant improvement in performance on multiprocessor computer clusters. We applied this method to a difficult polyatomic clusters problem in computational chemistry, and found this method to outperform other algorithms.

Depressed mood and n-3 polyunsaturated fatty acid intake from fish: non-linear or confounded association?

There is increasing evidence of an association between low dietary intake of essential n-3 long chain polyunsaturated fatty acids (n-3 EFAs) and depressed mood. This study aimed to evaluate this association in a large population-based sample of UK individuals. N-3 EFA intake (intake from fish alone, and from all sources (fish and supplements)), depressed mood (assessed using the short-form Depression, Anxiety and Stress Scales) and demographic variables (sex, age, Index of Multiple Deprivation (IMD) based on postal code, and date of questionnaire completion) were obtained simultaneously by self-report questionnaire (N = 2982). Using polynomial regression, a non-linear relationship between depressed mood and n-3 EFA intake from fish was found, with the incremental decrease in depressed mood diminishing as n-3 EFA intake increased. However, this relationship was attenuated by adjustment for age and IMD. No relationship between depression and n-3 EFA intake from all sources was found. These findings suggest that higher levels of n-3 EFA intake from fish are associated with lower levels of depressed mood, but the association disappears after adjustment for age and social deprivation, and after inclusion of n-3 EFA intake from supplements. This study does have a number of limitations, but the findings available suggest that the apparent associations between depressed mood and n-3 EFA intake from fish may simply reflect a wider association between depressed mood and lifestyle.

Job stress in the law enforcement sector: comparing the linear, non-linear and interaction effects of working conditions

This study addresses a gap in much of the research involving stress among high-risk occupations by investigating the effects of linear, non-linear and interaction models in a law enforcement organization that has undertaken a series of efficiency-driven organizational reforms. The results of a survey involving 2085 police officers indicated that the demand-control-support model provided good utility in predicting an officer's satisfaction, commitment and well-being. In particular, social support and job control were closely associated with all three outcome variables. Although the demand × control/support interactions were not identified in the data, there was some support for the curvilinear effects of job demands. The results have implications for the organizational conditions that need to be addressed in contemporary policing environments where new public management strategies have had widespread affects on the social and organizational context in which policing takes place.

Identifying the predictors of employee health and satisfaction in an NPM environment : testing a comprehensive and non-linear demand-control-support model

The Demand-Control-Support (DCS) model is investigated in the context of police officers working within an organization that has relatively widespread uptake of New Public Management (NPM) practices. A survey of 479 police officers from two geographic regions was undertaken and the results indicate that the DCS offers a simple, yet powerful, framework for identifying the conditions to be managed in an NPM-oriented environment. Job control and work-based support predict all four target variables, strengthening the view that decision-making latitude and support from supervisors and colleagues represent critical resources for promoting the well-being, satisfaction and commitment of public sector employees.

Non-linear effects of landscape properties on mistletoe parasitism in fragmented agricultural landscapes

Ecological processes such as plant–animal interactions have a critical role in shaping the structure and function of ecosystems, but little is known of how such processes are modified by changes in landscape structure. We investigated the effect of landscape change on mistletoe parasitism in fragmented agricultural environments by surveying mistletoes on eucalypt host trees in 24 landscapes, each 100 km² in size, in south-eastern Australia. Landscapes were selected to represent a gradient in extent (from 60% to 2% cover) and spatial pattern of remnant wooded vegetation. Mistletoes were surveyed at 15 sites in each landscape, stratified to sample five types of wooded elements in proportion to their relative cover. The incidence per landscape of box mistletoe (Amyema miquelii), the most common species, was best explained by the extent of wooded cover (non-linear relationship) and mean annual rainfall. Higher incidence occurred in landscapes with intermediate levels of cover (15–30%) and higher rainfall (>500 mm). Importantly, a marked non-linear decline in the incidence of A. miquelii in low-cover landscapes implies a disproportionate loss of this species in remaining wooded vegetation, greater than that attributable to decreasing forest cover. The most likely mechanism is the effect of landscape change on the mistletoebird (Dicaeum hirundinaceum), the primary seed-dispersal vector for A. miquelii. Our results are consistent with observations that habitat fragmentation initially enhances mistletoe occurrence in agricultural environments; but in this region, when wooded vegetation fell below a threshold of ~15% landscape cover, the incidence of A. miquelii declined precipitously. Conservation management will benefit from greater understanding of the components of landscape structure that most influence ecological processes, such as mistletoe parasitism and other plant–animal mutualisms, and the critical stages in such relationships. This will facilitate action before critical thresholds are crossed and cascading effects extend to other aspects of ecosystem function.

A state space based approach in non-linear hemodynamic response modeling with fMRI data

In this paper we use the modified and integrated version of the balloon model in the analysis of fMRI data. We propose a new state space model realization for this balloon model and represent it with the standard A,B,C and D matrices widely used in system theory. A second order Padé approximation with equal numerator and denominator degree is used for the time delay approximation in the modeling of the cerebral blood flow. The results obtained through numerical solutions showed that the new state space model realization is in close agreement to the actual modified and integrated version of the balloon model. This new system theoretic formulation is likely to open doors to a novel way of analyzing fMRI data with real time robust estimators. With further development and validation, the new model has the potential to devise a generalized measure to make a significant contribution to improve the diagnosis and treatment of clinical scenarios where the brain functioning get altered. Concepts from system theory can readily be used in the analysis of fMRI data and the subsequent synthesis of filters and estimators.

Rock slope risk analysis based on non-linear failure criterion

The probability of failure of a rock slope is generally estimated by using the Limit Equilibrium Method (LEM) in conjunction with a reliability analysis. Although the LEM is relatively simple and time efficient, recent studies have indicated that using the LEM may overestimate the factor of safety by 21%, when based on a non-linear failure criterion. Fortunately, the solutions presented by Li et al. (2008, 2009) can provide more accurate evaluations for rock slope stability as the numerical upper and lower bound limit analysis methods (2002a, 2002b, 2005) were employed. The advantages of these methods are used in this study to assess the rock slope probability of failure. The motivation is that with more accurate methods to evaluate the factor of safety, more economic designs can be performed.

A non-linear programming-based similarity reasoning scheme for modelling of monotonicity-preserving multi-input fuzzy inference systems

In this paper, the zero-order Sugeno Fuzzy Inference System (FIS) that preserves the monotonicity property is studied. The sufficient conditions for the zero-order Sugeno FIS model to satisfy the monotonicity property are exploited as a set of useful governing equations to facilitate the FIS modelling process. The sufficient conditions suggest a fuzzy partition (at the rule antecedent part) and a monotonically-ordered rule base (at the rule consequent part) that can preserve the monotonicity property. The investigation focuses on the use of two Similarity Reasoning (SR)-based methods, i.e., Analogical Reasoning (AR) and Fuzzy Rule Interpolation (FRI), to deduce each conclusion separately. It is shown that AR and FRI may not be a direct solution to modelling of a multi-input FIS model that fulfils the monotonicity property, owing to the difficulty in getting a set of monotonically-ordered conclusions. As such, a Non-Linear Programming (NLP)-based SR scheme for constructing a monotonicity-preserving multi-input FIS model is proposed. In the proposed scheme, AR or FRI is first used to predict the rule conclusion of each observation. Then, a search algorithm is adopted to look for a set of consequents with minimized root means square errors as compared with the predicted conclusions. A constraint imposed by the sufficient conditions is also included in the search process. Applicability of the proposed scheme to undertaking fuzzy Failure Mode and Effect Analysis (FMEA) tasks is demonstrated. The results indicate that the proposed NLP-based SR scheme is useful for preserving the monotonicity property for building a multi-input FIS model with an incomplete rule base.

Global non-smooth optimization in robust multivariate regression

Robust regression in statistics leads to challenging optimization problems. Here, we study one such problem, in which the objective is non-smooth, non-convex and expensive to calculate. We study the numerical performance of several derivative-free optimization algorithms with the aim of computing robust multivariate estimators. Our experiences demonstrate that the existing algorithms often fail to deliver optimal solutions. We introduce three new methods that use Powell's derivative-free algorithm. The proposed methods are reliable and can be used when processing very large data sets containing outliers.