1,513 research outputs found
Some lower bounds on sparse outer approximations of polytopes
Motivated by the need to better understand the properties of sparse
cutting-planes used in mixed integer programming solvers, the paper [2] studied
the idealized problem of how well a polytope is approximated by the use of
sparse valid inequalities. As an extension to this work, we study the following
less idealized questions in this paper: (1) Are there integer programs, such
that sparse inequalities do not approximate the integer hull well even when
added to a linear programming relaxation? (2) Are there polytopes, where the
quality of approximation by sparse inequalities cannot be significantly
improved by adding a budgeted number of arbitrary (possibly dense) valid
inequalities? (3) Are there polytopes that are difficult to approximate under
every rotation? (4) Are there polytopes that are difficult to approximate in
all directions using sparse inequalities? We answer each of the above questions
in the positive
Mixed-integer Quadratic Programming is in NP
Mixed-integer quadratic programming is the problem of optimizing a quadratic
function over points in a polyhedral set where some of the components are
restricted to be integral. In this paper, we prove that the decision version of
mixed-integer quadratic programming is in NP, thereby showing that it is
NP-complete. This is established by showing that if the decision version of
mixed-integer quadratic programming is feasible, then there exists a solution
of polynomial size. This result generalizes and unifies classical results that
quadratic programming is in NP and integer linear programming is in NP
Impact of Internet gambling on problem gambling among adolescents in Italy: Findings from a large-scale nationally representative survey
Aims: The primary aim of the present study was to understand the impact of online gambling on gambling problems in a large-scale nationally representative sample of Italian youth, and to identify and then further examine a subgroup of online gamblers who reported higher rates of gambling problems. Design: Data from the ESPADÂźItalia2013 (European School Survey Project on Alcohol and Other Drugs) Study were used for analyses of adolescent Internet gambling. Setting: Self-administered questionnaires were completed by a representative sample of high school students, aged 15â19 years. Participants: A total of 14,778 adolescent students. Measurements: Respondentsâ problem gambling severity; gambling behavior (participation in eight different gambling activities, the number of gambling occasions and the number of online gambling occasions, monthly gambling expenditure); Socio-demographics (e.g., family structure and financial status); and control variables were measured individually (i.e., use of the Internet for leisure activities and playing video games). Findings: Rates of problem gambling were five times higher among online gamblers than non-online gamblers. In addition, factors that increased the risk of becoming a problem online gambler included living with non-birth parents, having a higher perception of financial family status, being more involved with gambling, and the medium preferences of remote gamblers (e.g., Internet cafes, digital television, and video game console). Conclusions: The online gambling environment may pose significantly greater risk to vulnerable players. Family characteristics and contextual elements concerning youth Internet gambling (e.g., remote mediums) may play a key role in explaining problem online gambling among adolescents
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