Abstract A method of Sequential Log-Convex Programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical Geometric (GP) combined with ability Quadratic Program (SQP) to accommodate a wide range objective and constraint functions, resulting practical algorithm can be adopted little no modification existing practices. Three ...

We present a planar point location structure for a convex subdivision S. Given a query sequence of length m, the total running time is O(OPT + m log log n + n), where n is the number of vertices in S and OPT is the minimum time required by any linear decision tree for answering planar point location queries in S to process the same query sequence. The running time includes the preprocessing tim...

In this paper, we construct upper and lower convex order bounds for the distribution of a sum of non-independent log-elliptical random variables. These bounds are applications of the ideas developed in Kaas, Dhaene & Goovaerts (2000). The class of multivariate log-elliptical random variables is an extension of the class of multivariate log-normal random variables. Hence, the results presented h...

In this paper, we investigate the online non-convex optimization problem which generalizes the classic online convex optimization problem by relaxing the convexity assumption on the cost function. For this type of problem, the classic exponential weighting online algorithm has recently been shown to attain a sub-linear regret of O( √ T log T ). In this paper, we introduce a novel recursive stru...

We present a new data structure for a set of n convex simply-shaped fat objects in the plane, and use it to obtain eecient and rather simple solutions to several problems including (i) vertical ray shooting | preprocess a set K of n non-intersecting convex simply-shaped at objects in 3-space, whose xy-projections are fat, for eecient vertical ray shooting queries, (ii) point enclosure | preproc...

We present eecient algorithms for shortest-path and minimum-link-path queries between two convex polygons inside a simple polygon P, which acts as an obstacle to be avoided. Let n be the number of vertices of P, and h the total number of vertices of the query polygons. We show that shortest-path queries can be performed optimally in time O(log h + logn) (plus O(k) time for reporting the k edges...

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.

This abstract presents a first step towards kinetic collision detection in 3 dimensions. In particular, we design a compact and responsive kinetic data structure (KDS) for detecting collisions between n balls of arbitrary sizes rolling on a plane. The KDS has size O(n log n) and can handle events in O(log n) time. The structure processes O(n) events in the worst case, assuming that the objects ...

This abstract presents a first step towards kinetic collision detection in 3 dimensions. In particular, we design a compact and responsive kinetic data structure (KDS) for detecting collisions between n balls of arbitrary sizes rolling on a plane. The KDS has size O(n log n) and can handle events in O(log n) time. The structure processes O(n) events in the worst case, assuming that the objects ...

We develop geometric optimisation on the manifold of hermitian positive definite (hpd) matrices. In particular, we consider optimising two types of cost functions: (i) geodesically convex (g-convex); and (ii) log-nonexpansive (LN). G-convex functions are nonconvex in the usual euclidean sense, but convex along the manifold and thus allow global optimisation. LN functions may fail to be even g-c...