we introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition fo...

We investigate the Kramers-Wannier approximation for the three-dimensional (3D) Ising model. The variational state is represented by an effective 2D Ising model, which contains two variational parameters. We numerically calculate the variational partition function using the corner transfer matrix renormalization group (CTMRG) method, and find its maximum with respect to the variational paramete...

The path planning problem, i.e., the geometrical problem of finding a collision-free path between two given configurations of a robot moving among obstacles, has been studied by many authors in recent years. Several complete algorithms exist for robots with few degrees of freedom (DOF), but they are intractable for more than 4 DOF. In order to tackle problems in higher dimensions, several heuri...

Based on the concept of discontinuity displacement, an analytical solution for cracked thin plates has been derived in which displacements and stresses in a solid can be expressed by the linear distributed discontinuity displacements on the whole boundary. By way of the potential variational principle and the analytical solution newly developed, a boundary element model for 2D multiple crack pr...

It’s shown that a number of variational problems can be cast as finding the maxinf-points (or minsup-points) of bivariate functions, coveniently abbreviated to bifunctions. These variational problems include: linear and nonlinear complementarity problems, fixed points, variational inequalities, inclusions, non-cooperative games, Walras and Nash equilibrium problems. One can then appeal to the t...

The Geodesic Active contour model is a very flexible model for variational image segmentation. Unfortunately the Geodesic Active Contour model exhibits local minima making segmentation results strongly dependent on its initialization. We propose a flexible, interactive segmentation method in two and three dimensions that yields the globally optimal solution with respect to local constraints int...

A Γ-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane...

In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. this case, by exploiting a Fourier expansion along azimuthal direction, fully three-dimensional (3D) calculations can be carried out on two-dimensional (2D) angular cross section of problem, thus significantly reducing computational effort. However, transition from full 3D problem to 2D anal...

The applications of symmetry groups to problems arising in the calculus of variations have their origins in the late papers of Lie, e.g., [34], which introduced the subject of “integral invariants”. Lie showed how the symmetry group of a variational problem can be readily computed based on an adaptation of the infinitesimal method used to compute symmetry groups of differential equations. Moreo...