We study a boundary value problem associated with a system of two second order differential equations with cubic nonlinearity which model a film of superconductor material subjected to a tangential magnetic field. We show that for an appropriate range of parameters there are asymmetric solutions, and only trivial symmetric solutions. We then correct an error of the authors in [9] and show that ...

The variable projection algorithm of Golub and Pereyra (1973) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more importantly, a better likelihood of finding a global minimizer rather than a local one. The purpose of our work is to provide a more robust implementat...

A methodology is developed for the numerical solution to the sample-based optimal transport and Wasserstein barycenter problems. The procedure is based on a characterization of the barycenter and of the McCann interpolants that permits the decomposition of the global problem under consideration into various local problems where the distance among successive distributions is small. These local p...

We present a vectorial self dual morphological filter. Contrary tomanymethods, our approach does not require the use of an ordering on vectors. It relies on theminimization of the total variationwithL norm as data fidelity on each channel. We further constraint this minimization in order not to create new values. It is shown that this minimization yields a self-dual and contrast invariant filte...

Automatic generation of smooth, non-overlapping meshes on arbitrary regions is the well-known problem. Considered as optimization task the problem may be reduced to finding a minimizer of the weighted combination of so-called length, area, and orthogonality functionals. Unfortunately, it has been shown that on the one hand, certain weights of the individual functionals do not admit the unique o...

An Ant Colony System (ACS) minimizer is implemented for the solution of the inverse radiative transfer problem associated to the estimation of the optical thickness, single scattering albedo and boundary surfaces diffuse reflectivities in a one-dimensional homogeneous medium. The ACS minimizer was implemented in a PC cluster using the MPI library yielding good speed-up and efficiency results. A...

This paper studies loss functions for finite sets. For a given set S, we give sum-of-square type of minimum degree. When S is the vertex standard simplex, show such have no spurious minimizers (i.e., every local minimizer global one). Up to transformations, similar without general approximately by sample T, how get solving quadratic optimization problem. Numerical experiments and applications a...

The dynamics of randomly forced Burgers and Euler-Lagrange equations in S 1 × R d−1 in the case when there is only one one-sided minimizer in a compact subset of S 1 × R d−1 is studied. The existence of random invariant periodic minimizer orbits and periodicity of the stationary solution of the stochastic Burgers equations are obtained.

A a set-valued optimization problem minC F (x), x ∈ X0, is considered, where X0 ⊂ X , X and Y are Banach spaces, F : X0 Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x, y), y ∈ F (x), and are called minimizers. In particular the notions ofw-minimizer (weakly efficient points), p-minimizer (properly efficient points) and i-mi...

We consider the minimization of an energy functional given by sum a crystalline perimeter and nonlocal interaction Riesz type, under volume constraint. show that, in small mass regime, if Wulff shape anisotropic has certain symmetry properties, then it is unique global minimizer total energy. In dimension two this applies to convex polygons which are reflection symmetric with respect bisectors ...