A Branch and Bound algorithm for general mixed-integer quadratic programs based on quadratic convex relaxation

Let \((MQP)\) be a general mixed-integer quadratic program that consists of minimizing a quadratic function \(f(x) = x^TQx +c^Tx\) subject to linear constraints. Our approach to solve \((MQP)\) is first to consider an equivalent general mixed-integer quadratic problem. This equivalent problem has additional variables \(y_{ij}\) , additional quadratic constraints \(y_{ij}=x_ix_j\) , a convex objective function, and a set of valid inequalities. Contrarily to the reformulation proposed in Billionnet et al. (Math Program 131(1):381–401, 2012), the equivalent problem cannot be directly solved by a standard solver. Here, we propose a new Branch and Bound process based on the relaxation of the non-convex constraints \(y_{ij}=x_ix_j\) to solve \((MQP)\) . Computational experiences are carried out on pure- and mixed-integer quadratic instances. The results show that the solution time of most of the considered instances with up to 60 variables is improved by our Branch and Bound algorithm in comparison with the approach of Billionnet et al. (2012) and with the general mixed-integer nonlinear solver BARON (Sahinidis and Tawarmalani, Global optimization of mixed-integer nonlinear programs, user’s manual, 2010).     

Gender differences in disability-free life expectancy for selected risk factors and chronic conditions in Canada

This article shows how mortality and morbidity patterns differ for women and men 45 years of age and older. The impact on disability-free life expectancy was calculated for selected risk factors and chronic conditions: low income, low education, abnormal body mass index, lack of physical activity, smoking, cancer, diabetes, and arthritis. For each factor, the expected number of years free of disability was calculated for men and women using multi-state life tables. In terms of disability-free life expectancy, the greatest impacts on affected women were for diabetes (14.1 years), arthritis (8.8 years), and physical inactivity (6.0 years), while for affected men, the greatest impacts were for diabetes (10.5 years), smoking (6.9 years), arthritis (6.5 years), and cancer (6.4 years). The implications of these results are discussed from the perspective of developing programs designed to improve population health status.     

Risk seeking with diminishing marginal utility in a non-expected utility model

The present work takes place in the framework of a non-expected utility model under risk: the RDEU theory (Rank Dependent Expected Utility, first initiated by Quiggin under the denomination of Anticipated Utility), where the decision maker's behavior is characterized by two functionsu andf. Our first result gives a condition under which the functionu characterizes the decision maker's attitude towards wealth. Then, defining a decision maker as risk averter (respectively risk seeker) when he always prefers to any random variable its expected value (weak definition of risk aversion), the second result states that a decision maker who has an increasing marginal utility of wealth (a convex functionu) can be risk averse, if his functionf issufficiently below his functionu, hence if he is sufficientlypessimistic. Obviously, he can also be risk seeking with a diminishing marginal utility of wealth. This result is noteworthy because with a stronger definition of risk aversion/risk seeking, based on mean-preserving spreads, Chew, Karni, and Safra have shown that the only way to be risk averse (in their sense) in RDEU theory is to have, simultaneously, a concave functionu and a convex functionf.     

Recognizing experiential knowledge in the process of qualification of peer helpers: an analysis of an educational program for service users in France

ABSTRACT

This article analyzes an innovative training program enabling the qualification of peer carers, working within the sector of ‘social inclusion’. Since the French national debate on social work conducted within the ‘Estates General’ of 2015, peer workers have become key players in training programs in virtue of their experiential knowledge and their understanding of issues related to the process of social exclusion. This article addresses the role of peer helpers’ experiential knowledge in the training process. Because of their ‘experiential’ and ‘empirical’ knowledge about questions linked to the process of exclusion, peer helpers have become key players in social work teams and within social institutions, thus contributing to new methods of socio-educational intervention. What impact will this recognition of peer helpers’ and service users’ experiential knowledge have on education in social work? This article gives an account of an 8-month training program for peer helpers examined on the methodological level through a process of Participant observation, and based on data from comprehensive interviews carried out with a panel of peer helpers.     

Test of Normality Against Generalized Exponential Power Alternatives

The family of symmetric generalized exponential power (GEP) densities offers a wide range of tail behaviors, which may be exponential, polynomial, and/or logarithmic. In this article, a test of normality based on Rao's score statistic and this family of GEP alternatives is proposed. This test is tailored to detect departures from normality in the tails of the distribution. The main interest of this approach is that it provides a test with a large family of symmetric alternatives having non-normal tails. In addition, the test's statistic consists of a combination of three quantities that can be interpreted as new measures of tail thickness. In a Monte-Carlo simulation study, the proposed test is shown to perform well in terms of power when compared to its competitors.     

Using large data sets to forecast sectoral employment

We use several models using classical and Bayesian methods to forecast employment for eight sectors of the US economy. In addition to using standard vector-autoregressive and Bayesian vector autoregressive models, we also augment these models to include the information content of 143 additional monthly series in some models. Several approaches exist for incorporating information from a large number of series. We consider two multivariate approaches—extracting common factors (principal components) and Bayesian shrinkage. After extracting the common factors, we use Bayesian factor-augmented vector autoregressive and vector error-correction models, as well as Bayesian shrinkage in a large-scale Bayesian vector autoregressive models. For an in-sample period of January 1972 to December 1989 and an out-of-sample period of January 1990 to March 2010, we compare the forecast performance of the alternative models. More specifically, we perform ex-post and ex-ante out-of-sample forecasts from January 1990 through March 2009 and from April 2009 through March 2010, respectively. We find that factor augmented models, especially error-correction versions, generally prove the best in out-of-sample forecast performance, implying that in addition to macroeconomic variables, incorporating long-run relationships along with short-run dynamics play an important role in forecasting employment. Forecast combination models, however, based on the simple average forecasts of the various models used, outperform the best performing individual models for six of the eight sectoral employment series.     

Revealed versus hidden attributes as determinants of percieved product quality

Consumers' quality perception being interpreted as an overall product evaluation process, attribute importance is introduced as a mediating variable between the quality judgment and informational value of cues. Furthermore, all product attribute being classified into two different categories, revealed vs. hidden attributes, it is hypothesized that extrinsic cues can influence consumers' product evaluation only on the hidden quality attributes but not on the revealed quality attributes.     

The impossibility of a Paretian egalitarian

In a one-good world, there is a nice correspondence between the Pigou-Dalton principle of transfer and social welfare dominance. In this paper we study the case of multiple goods (without using prices as a means to come back to one dimension), and show that many results of the one-dimensional setting carry over to the multidimensional case when individuals are assumed to have identical preferences. But the nice correspondence breaks down as soon as individual preferences display minimal differences, and multidimensional versions of the transfer principle clash with the Pareto principle. This analysis reveals an interesting connection with the theory of fair allocation, since multidimensional transfer principles are closely related to the no-domination criterion, a weak version of the no-envy criterion.For helpful comments, we thank J. L. Castillo, M. Le Breton, Y. Sprumont, K. Suzumura and participants at a workshop in Osnabrück, a LivinTax conference in Bordeaux and a seminar in Hitotsubashi University, as well as two referees. Financial support from TMR project Living Standards, Inequality and Taxation Contract no ERBFMXCT 980248 of the European Commission is gratefully acknowledged. We thank Michel Le Breton for giving us the permission to state a result contained in his unpublished Ph D thesis.     

Dialogues or polemics: Social science expertise and welfare reform in Quebec

The development of social assistance and poverty reduction policies has been informed by social scientific knowledge. Social scientists, however, are not of one mind on such matters. They tend to be divided along disciplinary and ideological lines and may even foster political divisions and conflicts. This article draws on the author's experience as an academic policy adviser to the Quebec government to analyse from up close the institutional context that facilitates knowledge utilisation in the policy process. Two reform processes are considered: the first one, between 1995 and 1998, was less collaborative and led to divisions, and the second, between 1997 and 2009, involved more interactions with the civil service and proved more fruitful. In both cases, experts were divided, as were politicians and civil servants, but their capacity to reach a consensus was fostered, in the second case, by better support and collaboration from the government.