A set of planar objects is said to be of type m if the convex hull of any two objects has its size bounded by 2m. In this paper, we present an algorithm based on the marriage-before-conquest paradigm to compute the convex hull of a set of n planar convex objects of xed type m. The algorithm is output-sensitive, i.e. its time complexity depends on the size h of the computed convex hull. The main...

We develop a variant of multiclass logistic regression that achieves three properties: i) We minimize a non-convex surrogate loss which makes the method robust to outliers, ii) our method allows transitioning between non-convex and convex losses by the choice of the parameters, iii) the surrogate loss is Bayes consistent, even in the non-convex case. The algorithm has one weight vector per clas...

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal s...

Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

visual servoing is generally contained of control and feature tracking. study of previous methods shows that no attempt has been made to optimize these two parts together. in kernel based visual servoing method, the main objective is to combine and optimize these two parts together and to make an entire control loop. this main target is accomplished by using lyapanov theory. a lyapanov candidat...

Let f be a (random) real-valued function whose graph represents the boundary of the convex hull of planar Brownian motion run until time 1 near its lowest point in a coordinate system so that f is non-negative and f(0) = 0. The ratio of f(x) and |x|/ | log |x|| oscillates near 0 between 0 and infinity a.s. 1. Main results. Let X = (X1, X2) be a 2-dimensional Brownian motion and let C denote the...

We study the projection of an element fractional Gaussian noise onto its neighbouring elements. prove some analytic results for coefficients this projection. In particular, we obtain recurrence relations them. also make several conjectures concerning behaviour these coefficients, provide numerical evidence supporting conjectures, and them theoretically in particular cases. As auxiliary result i...

A convex hole (or empty convex polygon) of a point set P in the plane is a convex polygon with vertices in P , containing no points of P in its interior. Let R be a bounded convex region in the plane. We show that the expected number of vertices of the largest convex hole of a set of n random points chosen independently and uniformly over R is Θ(logn/(log log n)), regardless of the shape of R.

We consider the problem of bounding from above the log-partition function corresponding to second-order Ising models for binary distributions. We introduce a new bound, the cardinality bound, which can be computed via convex optimization. The corresponding error on the logpartition function is bounded above by twice the distance, in model parameter space, to a class of “standard” Ising models, ...

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...