Traversing non-convex regions

Continuous Steepest Descent Path for Traversing Non-convex Regions

This paper revisits the ideas of seeking unconstrained minima by following a continuous steepest descent path (CSDP). We are especially interested in the merits of such an approach in regions where the objective function is non-convex and Newton-like methods become ineffective. The paper combines ODE-trajectory following with trust-region ideas to give an algorithm which performs curvilinear se...

The Delta Tree: An Object-Centered Approach to Image-Based Rendering

This paper introduces the delta tree, a data structure that represents an object using a set of reference images. It also describes an algorithm for generating arbitrary re-projections of an object by traversing its delta tree. Delta trees are an efficient representation in terms of both storage and rendering performance. Each node of a delta tree stores an image taken from a point on a samplin...

Non convex technologies and economic efficiency measure with imprecise data

The DNA Inequality in Non-Convex Regions

The DNA Inequality states that the average curvature of a curve inside of a given closed figure exceeds the average curvature of the figure. In the paper by Lagarias and Richardson (1997) that proved it for convex figures, the question arose if it could be possible to prove it for some non-convex region; the authors suggested L-Shaped regions. In this paper, we disprove the conjecture for L-Sha...

MULTIPLE PERIODIC SOLUTIONS FOR A CLASS OF NON-AUTONOMOUS AND CONVEX HAMILTONIAN SYSTEMS

In this paper we study Multiple periodic solutions for a class of non-autonomous and convex Hamiltonian systems and we investigate use some properties of Ekeland index.