For a $\mathcal{C}^2$-smooth function on a finite-dimensional space, a necessary condition for it... more For a $\mathcal{C}^2$-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for $\mathcal{C}^{1,1}$-smooth functions by using the Fr\'echet and Mordukhovich second-order subdifferentials.
This paper proposes and justifies two new globally convergent Newton-type methods to solve uncons... more This paper proposes and justifies two new globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class C1,1, or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of the Levenberg-Marquardt type being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence rates for both methods are at least linear, but becomes superlinear under the so-cal...
This paper aims to estimate the prevalence of cigarette smoking among students in Vietnam ages 13... more This paper aims to estimate the prevalence of cigarette smoking among students in Vietnam ages 13-15 and examines its relationship with compositional and contextual factors. The data used in this paper were obtained from the 2007 Global Youth Tobacco Survey conducted in nine provinces in Vietnam. A multilevel logistic regression model was applied to analyse the association between the current incidence of cigarette smoking and factors on both the individual and school level. The prevalence of cigarette smoking among students was 3.3% overall. The prevalence of smoking among male students (5.9%) was higher than that among females (1.2%). Parental smoking was a significant risk factor for smoking among the students. Having a friend who smoked was the strongest predictor of smoking status among the study subjects. We have demonstrated that school-level factors appeared to impact the prevalence of cigarette smoking among students ages 13-15. This paper highlights the importance of utilising an extensive range of actions to prevent students from using tobacco in Vietnam. These actions should include providing specific curricula for students that address both individual characteristics and the school environment. Further, prevention programmes should also target both parental- and peer-smoking issues.
For a $\mathcal{C}^2$-smooth function on a finite-dimensional space, a necessary condition for it... more For a $\mathcal{C}^2$-smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subspace orthogonal to its gradient, whereas a sufficient condition for its strict pseudoconvexity is the positive definiteness of its Hessian matrix on the subspace orthogonal to its gradient. Our aim in this paper is to extend those conditions for $\mathcal{C}^{1,1}$-smooth functions by using the Fr\'echet and Mordukhovich second-order subdifferentials.
This paper proposes and justifies two new globally convergent Newton-type methods to solve uncons... more This paper proposes and justifies two new globally convergent Newton-type methods to solve unconstrained and constrained problems of nonsmooth optimization by using tools of variational analysis and generalized differentiation. Both methods are coderivative-based and employ generalized Hessians (coderivatives of subgradient mappings) associated with objective functions, which are either of class C1,1, or are represented in the form of convex composite optimization, where one of the terms may be extended-real-valued. The proposed globally convergent algorithms are of two types. The first one extends the damped Newton method and requires positive-definiteness of the generalized Hessians for its well-posedness and efficient performance, while the other algorithm is of the Levenberg-Marquardt type being well-defined when the generalized Hessians are merely positive-semidefinite. The obtained convergence rates for both methods are at least linear, but becomes superlinear under the so-cal...
This paper aims to estimate the prevalence of cigarette smoking among students in Vietnam ages 13... more This paper aims to estimate the prevalence of cigarette smoking among students in Vietnam ages 13-15 and examines its relationship with compositional and contextual factors. The data used in this paper were obtained from the 2007 Global Youth Tobacco Survey conducted in nine provinces in Vietnam. A multilevel logistic regression model was applied to analyse the association between the current incidence of cigarette smoking and factors on both the individual and school level. The prevalence of cigarette smoking among students was 3.3% overall. The prevalence of smoking among male students (5.9%) was higher than that among females (1.2%). Parental smoking was a significant risk factor for smoking among the students. Having a friend who smoked was the strongest predictor of smoking status among the study subjects. We have demonstrated that school-level factors appeared to impact the prevalence of cigarette smoking among students ages 13-15. This paper highlights the importance of utilising an extensive range of actions to prevent students from using tobacco in Vietnam. These actions should include providing specific curricula for students that address both individual characteristics and the school environment. Further, prevention programmes should also target both parental- and peer-smoking issues.
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