Immobile indices and CQ-free optimality criteria for linear copositive programming problems

We consider problems of linear copositive programming where feasible sets consist of vectors for which the quadratic forms induced by the corresponding linear matrix combinations are nonnegative over the nonnegative orthant. Given a linear copositive problem, we define immobile indices of its constraints and a normalized immobile index set. We prove that the normalized immobile index set is either empty or can be represented as a union of a finite number of convex closed bounded polyhedra. We show that the study of the structure of this set and the connected properties of the feasible set permits to obtain new optimality criteria for copositive problems. These criteria do not require the fulfillment of any additional conditions (constraint qualifications or other). An illustrative example shows that the optimality conditions formulated in the paper permit to detect the optimality of feasible solutions for which the known sufficient optimality conditions are not able to do this. We apply the approach based on the notion of immobile indices to obtain new formulations of regularized primal and dual problems which are explicit and guarantee strong duality.publishe

The Great American Crime Decline : Possible Explanations

This chapter examines the most important features of the crime decline in the United States during the 1990s-2010s but also takes a broader look at the violence declines of the last three centuries. The author argues that violent and property crime trends might have diverged in the 1990s, with property crimes increasingly happening in the online sphere and thus traditional property crime statistics not being reflective of the full picture. An important distinction is made between ‘contact crimes’ and crimes that do not require a victim and offender to be present in the same physical space. Contrary to the uncertainties engendered by property crime, the declines in violent (‘contact’) crime are rather general, and have been happening not only across all demographic and geographic categories within the United States but also throughout the developed world. An analysis of research literature on crime trends has identified twenty-four different explanations for the crime drop. Each one of them is briefly outlined and examined in terms of conceptual clarity and empirical support. Nine crime decline explanations are highlighted as the most promising ones. The majority of these promising explanations, being relative newcomers in the crime trends literature, have not been subjected to sufficient empirical scrutiny yet, and thus require further research. One potentially fruitful avenue for future studies is to examine the association of the most promising crime decline explanations with improvements in self-control

Neighborhood Disadvantage and Changes in Condom Use Among African American Adolescents

OBJECTIVE: Risk factors for adolescent alcohol use are typically conceptualized as individual and interpersonal level factors; however, these factors do not fully explain adolescent drinking behavior. We used a socioecological model to examine the contribution of neighborhood factors in a risk and promotive model of adolescent alcohol use among urban high school youth (N = 711; 52% female; 82% African American; M = 18 years old). METHOD: Using a multilevel model, we considered the role of neighborhood disadvantage on youth alcohol use, after accounting for risk (e.g., peer and parental substance use) and promotive factors (e.g., social support and participation in prosocial activities). RESULTS: Peer alcohol use and peer support were associated with more alcohol use, and maternal support was negatively associated with alcohol use. Despite significant variation at the neighborhood level, neighborhood disadvantage was not directly associated with adolescent drinking. CONCLUSIONS: Our study contributes to a mixed body of literature on social context and adolescent health. Although our research highlights the importance of interpersonal relationships, we found no support for neighborhood influences. We conclude with future directions for research examining the link between adolescent drinking and neighborhood contexts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91269/1/Bauermeister_JUH_2011.pd