GLOBAL ANALYSIS OF ONE-DIMENSIONAL VARIATIONAL PROBLEMS

One dimensional infinite-horizon variational problems arising in viscoelasticity

Analysis of Two Dimensional Non Convex Variational Problems

The purpose of this work is to carry out the analysis of twodimensional scalar variational problems by the method of moments. This method is indeed shown to be useful for treating general cases in which the Lagrangian is a separable polynomial in the derivative variables. In these cases, it follows that the discretization of these problems can be reduced to a single large scale semidefinite pro...

Global Optimization for One-Dimensional Structure and Motion Problems

We study geometric reconstruction problems in one-dimensional retina vision. In such problems, the scene is modeled as a 2D plane, and the camera sensor produces 1D images of the scene. Our main contribution is an efficient method for computing the global optimum to the structure and motion problem with respect to the L∞ norm of the reprojection errors. One-dimensional cameras have proven usefu...

Solving infinite horizon optimization problems through analysis of a one-dimensional global optimization problem

Infinite horizon optimization (IHO) problems present a number of challenges for their solution, most notably, the inclusion of an infinite data set. This hurdle is often circumvented by approximating its solution by solving increasingly longer finite horizon truncations of the original infinite horizon problem. In this paper, we adopt a novel transformation that reduces the infinite dimensional...

Quasi - One - Dimensional Riemann Problems

We study two-dimensional Riemann problems with piecewise constant data. We identify a class of two-dimensional systems, including many standard equations of compressible ow, which are simpliied by a transformation to similarity variables. For equations in this class, a two-dimensional Riemann problem with sectorially constant data becomes a boundary-value problem in the nite plane. For data lea...