Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002a,b) have studied convex bounds for a sum of dependent random variables and applied these to sums of log-normal random variables. In particular, they have shown how these convex bounds can be used to derive closed-form approximations for several of the risk measures of such a sum. In this paper we investigate to which extent their general results on...

Given an input consisting of an n-vertex convex polygon with k hole vertices or an n-vertex planar straight line graph (PSLG) with k holes and/or reflex vertices inside the convex hull, the parameterized minimum number convex partition (MNCP) problem asks for a partition into a minimum number of convex pieces. We give a fixedparameter tractable algorithm for this problem that runs in the follow...

Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these in log-domain natural variation on this that our knowledge previously unstudied. In paper, we analyze methods and prove their polynomial-time convergence. We also they are approximated by classical barrier precise sense provide simple computational exper...

We establish the preserving log-convexity property for the generalized Pascal triangles. It is an extension of a result of H. Davenport and G. Pólya “On the product of two power series”, who proved that the binomial convolution of two log-convex sequences is log-convex.

Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $mathscr{B}$ (resp. $varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with  $mathscr{B}$ (resp. $varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbase...

We give a novel algorithm for stochastic strongly-convex optimization in the gradient oracle model which returns an O( 1 T )-approximate solution after T gradient updates. This rate of convergence is optimal in the gradient oracle model. This improves upon the previously known best rate of O( log(T ) T ), which was obtained by applying an online strongly-convex optimization algorithm with regre...

In this paper, we establish some new Hermite-Hadamard type integral inequalities involving two log-preinvex functions. Note that log-preinvex functions are nonconvex functions and include the log-convex functions as special cases. As special cases, we obtain the well known results for the convex functions.