In this paper, the existence of a solution in the form of a minimizer or microstructure is established for the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff type materials. Necessary and sufficient conditions for minimizing sequences of the potential energy to converge to a minimizer or to microstructure are ...

We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set Ω. We prove existence, regularity and some structural properties of minimizers. In particular, when Ω is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a minimizer with self-intersections.

Fusing a lower resolution color image with a higher resolution monochrome image is a common practice in medical imaging. By incorporating spatial context and/or improving the signal-to-noise ratio, it provides clinicians with a single frame of the most complete information for diagnosis. In this paper, image fusion is formulated as a convex optimization problem that avoids image decomposition a...

I Simple proof of linear convergence. I For convex functions, equivalent to several of the above conditions. I For non-convex functions, weakest assumption while still guaranteeing global minimizer. ? We generalize the PL condition to analyze proximal-gradient methods. ? We give simple new analyses in a variety of settings: I Least-squares and logistic regression. I Randomized coordinate descen...

A new hybrid algorithm is proposed in this paper. An independent task scheduling algorithm is designed based on the hybrid algorithm. The hybrid algorithm adopt list scheduling method to code harmony solution and convert harmony vector to priority-based independent task scheduling model, and perform variable neighborhood search on harmony solutions to improve Harmony Search efficiency and solut...

In this paper we compare two methods for estimating a global minimizer of an inde nite quadratic form over a simplex The rst method is based on the enumeration of local minimizers of a so called control polytope The second method is based on an approximation of the convex envelope using semide nite programming In order to test the algorithms a method for generating random test problems is prese...

We consider the problem of minimizing the energy functional R (|∇u|2 + χ{u>0}). We show that the singular axisymmetric critical point of the functional is an energy minimizer in dimension 7. This is the first example of a non-smooth energy minimizer. It is analogous to the Simons cone, a least area hypersurface in dimension 8.

We consider the problem of minimizing the bending or elastic energy among Jordan curves con ned in a given open set Ω. We prove existence, regularity and some structural properties of minimizers. In particular, when Ω is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a minimizer with self-intersections.

We apply the nonlinear generalized Rayleigh quotients method to develop new tools that can be used study ground states of Schrödinger equations. introduce a type variational functional, global minimizer which corresponds so-called fundamental frequency solutions with prescribed action value. find state problem and uniquely determine corresponding values mass, frequency, level. Based on this app...

We study the Wasserstein Hamiltonian flow with a common noise on density manifold of finite graph. Under framework stochastic variational principle, we first develop formulation and show local existence unique solution. also establish sufficient condition for global Consequently, obtain well-posedness nonlinear Schrödinger equations In addition, using Wong–Zakai approximation noise, prove minim...